diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index e1262879ba3b2..7628eaaddd336 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -18948,10 +18948,18 @@ namespace ts {
                     return indexTypesIdenticalTo(source, target, kind);
                 }
                 const targetType = getIndexTypeOfType(target, kind);
-                if (!targetType || targetType.flags & TypeFlags.Any && !sourceIsPrimitive && kind === IndexKind.String) {
-                    // Index signature of type any permits assignment from everything but primitives
+                if (!targetType) {
                     return Ternary.True;
                 }
+                if (targetType.flags & TypeFlags.Any && !sourceIsPrimitive) {
+                    // An index signature of type `any` permits assignment from everything but primitives,
+                    // provided that there is also a `string` index signature of type `any`.
+                    const stringIndexType = kind === IndexKind.String ? targetType : getIndexTypeOfType(target, IndexKind.String);
+                    if (stringIndexType && stringIndexType.flags & TypeFlags.Any) {
+                        return Ternary.True;
+                    }
+
+                }
                 if (isGenericMappedType(source)) {
                     // A generic mapped type { [P in K]: T } is related to a type with an index signature
                     // { [x: string]: U }, and optionally with an index signature { [x: number]: V },
diff --git a/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.errors.txt b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.errors.txt
new file mode 100644
index 0000000000000..20362a25942c1
--- /dev/null
+++ b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.errors.txt
@@ -0,0 +1,145 @@
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(43,5): error TS2322: Type 'Obj' is not assignable to type 'NumberTo<any>'.
+  Index signature is missing in type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(49,5): error TS2739: Type 'StringTo<any>' is missing the following properties from type 'Obj': hello, world
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(50,5): error TS2739: Type 'NumberTo<any>' is missing the following properties from type 'Obj': hello, world
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(51,5): error TS2739: Type 'StringAndNumberTo<any>' is missing the following properties from type 'Obj': hello, world
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(61,5): error TS2322: Type 'Obj' is not assignable to type 'NumberTo<any>'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(65,5): error TS2322: Type 'Obj' is not assignable to type 'StringTo<any> & NumberTo<any>'.
+  Type 'Obj' is not assignable to type 'NumberTo<any>'.
+    Index signature is missing in type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(67,5): error TS2322: Type 'StringTo<any>' is not assignable to type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(68,5): error TS2322: Type 'NumberTo<any>' is not assignable to type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(69,5): error TS2739: Type 'StringTo<any> & NumberTo<any>' is missing the following properties from type 'Obj': hello, world
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(84,5): error TS2322: Type 'Obj' is not assignable to type 'NumberToNumber'.
+  Index signature is missing in type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(88,5): error TS2322: Type 'Obj' is not assignable to type 'StringToAnyNumberToNumber'.
+  Index signature is missing in type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(90,5): error TS2322: Type 'StringTo<any>' is not assignable to type 'Obj'.
+tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts(91,5): error TS2739: Type 'NumberTo<number>' is missing the following properties from type 'Obj': hello, world
+
+
+==== tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts (13 errors) ====
+    // When checking compatibility between two types,
+    // TypeScript should not require an index signature if
+    // the target side index signature maps to `any` *and*
+    // the target side has *any* string index signature to `any`.
+    //
+    // So an index signature like in
+    //
+    //  { [x: number]: any }
+    //
+    // is still required of a source type, but neither index signature in
+    //
+    //  { [x: number]: any, [x: string]: any; }
+    //
+    // should be required; *however*, the number index signature in
+    //
+    //  { [x: number]: number, [x: string]: any; }
+    //
+    // should always be required.
+    
+    interface StringTo<T> {
+        [x: string]: T;
+    }
+    
+    interface NumberTo<T> {
+        [x: number]: T;
+    }
+    
+    interface StringAndNumberTo<T> extends StringTo<T>, NumberTo<T> {
+    }
+    
+    interface Obj {
+        hello: string;
+        world: number;
+    }
+    
+    function f1(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringAndNumberTo<any>, someObj: Obj) {
+        sToAny = nToAny;
+        sToAny = bothToAny;
+        sToAny = someObj;
+    
+        nToAny = sToAny;
+        nToAny = bothToAny;
+        nToAny = someObj;
+        ~~~~~~
+!!! error TS2322: Type 'Obj' is not assignable to type 'NumberTo<any>'.
+!!! error TS2322:   Index signature is missing in type 'Obj'.
+    
+        bothToAny = sToAny;
+        bothToAny = nToAny;
+        bothToAny = someObj;
+    
+        someObj = sToAny;
+        ~~~~~~~
+!!! error TS2739: Type 'StringTo<any>' is missing the following properties from type 'Obj': hello, world
+        someObj = nToAny;
+        ~~~~~~~
+!!! error TS2739: Type 'NumberTo<any>' is missing the following properties from type 'Obj': hello, world
+        someObj = bothToAny;
+        ~~~~~~~
+!!! error TS2739: Type 'StringAndNumberTo<any>' is missing the following properties from type 'Obj': hello, world
+    }
+    
+    function f2(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringTo<any> & NumberTo<any>, someObj: Obj) {
+        sToAny = nToAny;
+        sToAny = bothToAny;
+        sToAny = someObj;
+    
+        nToAny = sToAny;
+        nToAny = bothToAny;
+        nToAny = someObj;
+        ~~~~~~
+!!! error TS2322: Type 'Obj' is not assignable to type 'NumberTo<any>'.
+    
+        bothToAny = sToAny;
+        bothToAny = nToAny;
+        bothToAny = someObj;
+        ~~~~~~~~~
+!!! error TS2322: Type 'Obj' is not assignable to type 'StringTo<any> & NumberTo<any>'.
+!!! error TS2322:   Type 'Obj' is not assignable to type 'NumberTo<any>'.
+!!! error TS2322:     Index signature is missing in type 'Obj'.
+    
+        someObj = sToAny;
+        ~~~~~~~
+!!! error TS2322: Type 'StringTo<any>' is not assignable to type 'Obj'.
+        someObj = nToAny;
+        ~~~~~~~
+!!! error TS2322: Type 'NumberTo<any>' is not assignable to type 'Obj'.
+        someObj = bothToAny;
+        ~~~~~~~
+!!! error TS2739: Type 'StringTo<any> & NumberTo<any>' is missing the following properties from type 'Obj': hello, world
+    }
+    
+    type NumberToNumber = NumberTo<number>;
+    
+    interface StringToAnyNumberToNumber extends StringTo<any>, NumberToNumber {
+    }
+    
+    function f3(sToAny: StringTo<any>, nToNumber: NumberToNumber, strToAnyNumToNum: StringToAnyNumberToNumber, someObj: Obj) {
+        sToAny = nToNumber;
+        sToAny = strToAnyNumToNum;
+        sToAny = someObj;
+    
+        nToNumber = sToAny;
+        nToNumber = strToAnyNumToNum;
+        nToNumber = someObj;
+        ~~~~~~~~~
+!!! error TS2322: Type 'Obj' is not assignable to type 'NumberToNumber'.
+!!! error TS2322:   Index signature is missing in type 'Obj'.
+    
+        strToAnyNumToNum = sToAny;
+        strToAnyNumToNum = nToNumber;
+        strToAnyNumToNum = someObj;
+        ~~~~~~~~~~~~~~~~
+!!! error TS2322: Type 'Obj' is not assignable to type 'StringToAnyNumberToNumber'.
+!!! error TS2322:   Index signature is missing in type 'Obj'.
+    
+        someObj = sToAny;
+        ~~~~~~~
+!!! error TS2322: Type 'StringTo<any>' is not assignable to type 'Obj'.
+        someObj = nToNumber;
+        ~~~~~~~
+!!! error TS2739: Type 'NumberTo<number>' is missing the following properties from type 'Obj': hello, world
+        someObj = someObj;
+    }
\ No newline at end of file
diff --git a/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.js b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.js
new file mode 100644
index 0000000000000..17f3b6248fa59
--- /dev/null
+++ b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.js
@@ -0,0 +1,157 @@
+//// [objectTypeWithStringAndNumberIndexSignatureToAny.ts]
+// When checking compatibility between two types,
+// TypeScript should not require an index signature if
+// the target side index signature maps to `any` *and*
+// the target side has *any* string index signature to `any`.
+//
+// So an index signature like in
+//
+//  { [x: number]: any }
+//
+// is still required of a source type, but neither index signature in
+//
+//  { [x: number]: any, [x: string]: any; }
+//
+// should be required; *however*, the number index signature in
+//
+//  { [x: number]: number, [x: string]: any; }
+//
+// should always be required.
+
+interface StringTo<T> {
+    [x: string]: T;
+}
+
+interface NumberTo<T> {
+    [x: number]: T;
+}
+
+interface StringAndNumberTo<T> extends StringTo<T>, NumberTo<T> {
+}
+
+interface Obj {
+    hello: string;
+    world: number;
+}
+
+function f1(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringAndNumberTo<any>, someObj: Obj) {
+    sToAny = nToAny;
+    sToAny = bothToAny;
+    sToAny = someObj;
+
+    nToAny = sToAny;
+    nToAny = bothToAny;
+    nToAny = someObj;
+
+    bothToAny = sToAny;
+    bothToAny = nToAny;
+    bothToAny = someObj;
+
+    someObj = sToAny;
+    someObj = nToAny;
+    someObj = bothToAny;
+}
+
+function f2(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringTo<any> & NumberTo<any>, someObj: Obj) {
+    sToAny = nToAny;
+    sToAny = bothToAny;
+    sToAny = someObj;
+
+    nToAny = sToAny;
+    nToAny = bothToAny;
+    nToAny = someObj;
+
+    bothToAny = sToAny;
+    bothToAny = nToAny;
+    bothToAny = someObj;
+
+    someObj = sToAny;
+    someObj = nToAny;
+    someObj = bothToAny;
+}
+
+type NumberToNumber = NumberTo<number>;
+
+interface StringToAnyNumberToNumber extends StringTo<any>, NumberToNumber {
+}
+
+function f3(sToAny: StringTo<any>, nToNumber: NumberToNumber, strToAnyNumToNum: StringToAnyNumberToNumber, someObj: Obj) {
+    sToAny = nToNumber;
+    sToAny = strToAnyNumToNum;
+    sToAny = someObj;
+
+    nToNumber = sToAny;
+    nToNumber = strToAnyNumToNum;
+    nToNumber = someObj;
+
+    strToAnyNumToNum = sToAny;
+    strToAnyNumToNum = nToNumber;
+    strToAnyNumToNum = someObj;
+
+    someObj = sToAny;
+    someObj = nToNumber;
+    someObj = someObj;
+}
+
+//// [objectTypeWithStringAndNumberIndexSignatureToAny.js]
+"use strict";
+// When checking compatibility between two types,
+// TypeScript should not require an index signature if
+// the target side index signature maps to `any` *and*
+// the target side has *any* string index signature to `any`.
+//
+// So an index signature like in
+//
+//  { [x: number]: any }
+//
+// is still required of a source type, but neither index signature in
+//
+//  { [x: number]: any, [x: string]: any; }
+//
+// should be required; *however*, the number index signature in
+//
+//  { [x: number]: number, [x: string]: any; }
+//
+// should always be required.
+function f1(sToAny, nToAny, bothToAny, someObj) {
+    sToAny = nToAny;
+    sToAny = bothToAny;
+    sToAny = someObj;
+    nToAny = sToAny;
+    nToAny = bothToAny;
+    nToAny = someObj;
+    bothToAny = sToAny;
+    bothToAny = nToAny;
+    bothToAny = someObj;
+    someObj = sToAny;
+    someObj = nToAny;
+    someObj = bothToAny;
+}
+function f2(sToAny, nToAny, bothToAny, someObj) {
+    sToAny = nToAny;
+    sToAny = bothToAny;
+    sToAny = someObj;
+    nToAny = sToAny;
+    nToAny = bothToAny;
+    nToAny = someObj;
+    bothToAny = sToAny;
+    bothToAny = nToAny;
+    bothToAny = someObj;
+    someObj = sToAny;
+    someObj = nToAny;
+    someObj = bothToAny;
+}
+function f3(sToAny, nToNumber, strToAnyNumToNum, someObj) {
+    sToAny = nToNumber;
+    sToAny = strToAnyNumToNum;
+    sToAny = someObj;
+    nToNumber = sToAny;
+    nToNumber = strToAnyNumToNum;
+    nToNumber = someObj;
+    strToAnyNumToNum = sToAny;
+    strToAnyNumToNum = nToNumber;
+    strToAnyNumToNum = someObj;
+    someObj = sToAny;
+    someObj = nToNumber;
+    someObj = someObj;
+}
diff --git a/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.symbols b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.symbols
new file mode 100644
index 0000000000000..43187b5380d30
--- /dev/null
+++ b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.symbols
@@ -0,0 +1,247 @@
+=== tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts ===
+// When checking compatibility between two types,
+// TypeScript should not require an index signature if
+// the target side index signature maps to `any` *and*
+// the target side has *any* string index signature to `any`.
+//
+// So an index signature like in
+//
+//  { [x: number]: any }
+//
+// is still required of a source type, but neither index signature in
+//
+//  { [x: number]: any, [x: string]: any; }
+//
+// should be required; *however*, the number index signature in
+//
+//  { [x: number]: number, [x: string]: any; }
+//
+// should always be required.
+
+interface StringTo<T> {
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 19, 19))
+
+    [x: string]: T;
+>x : Symbol(x, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 20, 5))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 19, 19))
+}
+
+interface NumberTo<T> {
+>NumberTo : Symbol(NumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 21, 1))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 23, 19))
+
+    [x: number]: T;
+>x : Symbol(x, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 24, 5))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 23, 19))
+}
+
+interface StringAndNumberTo<T> extends StringTo<T>, NumberTo<T> {
+>StringAndNumberTo : Symbol(StringAndNumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 25, 1))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 27, 28))
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 27, 28))
+>NumberTo : Symbol(NumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 21, 1))
+>T : Symbol(T, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 27, 28))
+}
+
+interface Obj {
+>Obj : Symbol(Obj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 28, 1))
+
+    hello: string;
+>hello : Symbol(Obj.hello, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 30, 15))
+
+    world: number;
+>world : Symbol(Obj.world, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 31, 18))
+}
+
+function f1(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringAndNumberTo<any>, someObj: Obj) {
+>f1 : Symbol(f1, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 33, 1))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+>NumberTo : Symbol(NumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 21, 1))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+>StringAndNumberTo : Symbol(StringAndNumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 25, 1))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+>Obj : Symbol(Obj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 28, 1))
+
+    sToAny = nToAny;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+
+    sToAny = bothToAny;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+
+    sToAny = someObj;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+
+    nToAny = sToAny;
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+
+    nToAny = bothToAny;
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+
+    nToAny = someObj;
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+
+    bothToAny = sToAny;
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+
+    bothToAny = nToAny;
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+
+    bothToAny = someObj;
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+
+    someObj = sToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 12))
+
+    someObj = nToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 34))
+
+    someObj = bothToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 92))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 35, 57))
+}
+
+function f2(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringTo<any> & NumberTo<any>, someObj: Obj) {
+>f2 : Symbol(f2, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 51, 1))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+>NumberTo : Symbol(NumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 21, 1))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>NumberTo : Symbol(NumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 21, 1))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+>Obj : Symbol(Obj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 28, 1))
+
+    sToAny = nToAny;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+
+    sToAny = bothToAny;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+
+    sToAny = someObj;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+
+    nToAny = sToAny;
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+
+    nToAny = bothToAny;
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+
+    nToAny = someObj;
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+
+    bothToAny = sToAny;
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+
+    bothToAny = nToAny;
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+
+    bothToAny = someObj;
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+
+    someObj = sToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 12))
+
+    someObj = nToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+>nToAny : Symbol(nToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 34))
+
+    someObj = bothToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 99))
+>bothToAny : Symbol(bothToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 53, 57))
+}
+
+type NumberToNumber = NumberTo<number>;
+>NumberToNumber : Symbol(NumberToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 69, 1))
+>NumberTo : Symbol(NumberTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 21, 1))
+
+interface StringToAnyNumberToNumber extends StringTo<any>, NumberToNumber {
+>StringToAnyNumberToNumber : Symbol(StringToAnyNumberToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 71, 39))
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>NumberToNumber : Symbol(NumberToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 69, 1))
+}
+
+function f3(sToAny: StringTo<any>, nToNumber: NumberToNumber, strToAnyNumToNum: StringToAnyNumberToNumber, someObj: Obj) {
+>f3 : Symbol(f3, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 74, 1))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+>StringTo : Symbol(StringTo, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 0, 0))
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+>NumberToNumber : Symbol(NumberToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 69, 1))
+>strToAnyNumToNum : Symbol(strToAnyNumToNum, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 61))
+>StringToAnyNumberToNumber : Symbol(StringToAnyNumberToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 71, 39))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+>Obj : Symbol(Obj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 28, 1))
+
+    sToAny = nToNumber;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+
+    sToAny = strToAnyNumToNum;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+>strToAnyNumToNum : Symbol(strToAnyNumToNum, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 61))
+
+    sToAny = someObj;
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+
+    nToNumber = sToAny;
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+
+    nToNumber = strToAnyNumToNum;
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+>strToAnyNumToNum : Symbol(strToAnyNumToNum, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 61))
+
+    nToNumber = someObj;
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+
+    strToAnyNumToNum = sToAny;
+>strToAnyNumToNum : Symbol(strToAnyNumToNum, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 61))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+
+    strToAnyNumToNum = nToNumber;
+>strToAnyNumToNum : Symbol(strToAnyNumToNum, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 61))
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+
+    strToAnyNumToNum = someObj;
+>strToAnyNumToNum : Symbol(strToAnyNumToNum, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 61))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+
+    someObj = sToAny;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+>sToAny : Symbol(sToAny, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 12))
+
+    someObj = nToNumber;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+>nToNumber : Symbol(nToNumber, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 34))
+
+    someObj = someObj;
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+>someObj : Symbol(someObj, Decl(objectTypeWithStringAndNumberIndexSignatureToAny.ts, 76, 106))
+}
diff --git a/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.types b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.types
new file mode 100644
index 0000000000000..5c2efdc2bc007
--- /dev/null
+++ b/tests/baselines/reference/objectTypeWithStringAndNumberIndexSignatureToAny.types
@@ -0,0 +1,250 @@
+=== tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts ===
+// When checking compatibility between two types,
+// TypeScript should not require an index signature if
+// the target side index signature maps to `any` *and*
+// the target side has *any* string index signature to `any`.
+//
+// So an index signature like in
+//
+//  { [x: number]: any }
+//
+// is still required of a source type, but neither index signature in
+//
+//  { [x: number]: any, [x: string]: any; }
+//
+// should be required; *however*, the number index signature in
+//
+//  { [x: number]: number, [x: string]: any; }
+//
+// should always be required.
+
+interface StringTo<T> {
+    [x: string]: T;
+>x : string
+}
+
+interface NumberTo<T> {
+    [x: number]: T;
+>x : number
+}
+
+interface StringAndNumberTo<T> extends StringTo<T>, NumberTo<T> {
+}
+
+interface Obj {
+    hello: string;
+>hello : string
+
+    world: number;
+>world : number
+}
+
+function f1(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringAndNumberTo<any>, someObj: Obj) {
+>f1 : (sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringAndNumberTo<any>, someObj: Obj) => void
+>sToAny : StringTo<any>
+>nToAny : NumberTo<any>
+>bothToAny : StringAndNumberTo<any>
+>someObj : Obj
+
+    sToAny = nToAny;
+>sToAny = nToAny : NumberTo<any>
+>sToAny : StringTo<any>
+>nToAny : NumberTo<any>
+
+    sToAny = bothToAny;
+>sToAny = bothToAny : StringAndNumberTo<any>
+>sToAny : StringTo<any>
+>bothToAny : StringAndNumberTo<any>
+
+    sToAny = someObj;
+>sToAny = someObj : Obj
+>sToAny : StringTo<any>
+>someObj : Obj
+
+    nToAny = sToAny;
+>nToAny = sToAny : StringTo<any>
+>nToAny : NumberTo<any>
+>sToAny : StringTo<any>
+
+    nToAny = bothToAny;
+>nToAny = bothToAny : StringAndNumberTo<any>
+>nToAny : NumberTo<any>
+>bothToAny : StringAndNumberTo<any>
+
+    nToAny = someObj;
+>nToAny = someObj : Obj
+>nToAny : NumberTo<any>
+>someObj : Obj
+
+    bothToAny = sToAny;
+>bothToAny = sToAny : StringTo<any>
+>bothToAny : StringAndNumberTo<any>
+>sToAny : StringTo<any>
+
+    bothToAny = nToAny;
+>bothToAny = nToAny : NumberTo<any>
+>bothToAny : StringAndNumberTo<any>
+>nToAny : NumberTo<any>
+
+    bothToAny = someObj;
+>bothToAny = someObj : Obj
+>bothToAny : StringAndNumberTo<any>
+>someObj : Obj
+
+    someObj = sToAny;
+>someObj = sToAny : StringTo<any>
+>someObj : Obj
+>sToAny : StringTo<any>
+
+    someObj = nToAny;
+>someObj = nToAny : NumberTo<any>
+>someObj : Obj
+>nToAny : NumberTo<any>
+
+    someObj = bothToAny;
+>someObj = bothToAny : StringAndNumberTo<any>
+>someObj : Obj
+>bothToAny : StringAndNumberTo<any>
+}
+
+function f2(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringTo<any> & NumberTo<any>, someObj: Obj) {
+>f2 : (sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringTo<any> & NumberTo<any>, someObj: Obj) => void
+>sToAny : StringTo<any>
+>nToAny : NumberTo<any>
+>bothToAny : StringTo<any> & NumberTo<any>
+>someObj : Obj
+
+    sToAny = nToAny;
+>sToAny = nToAny : NumberTo<any>
+>sToAny : StringTo<any>
+>nToAny : NumberTo<any>
+
+    sToAny = bothToAny;
+>sToAny = bothToAny : StringTo<any> & NumberTo<any>
+>sToAny : StringTo<any>
+>bothToAny : StringTo<any> & NumberTo<any>
+
+    sToAny = someObj;
+>sToAny = someObj : Obj
+>sToAny : StringTo<any>
+>someObj : Obj
+
+    nToAny = sToAny;
+>nToAny = sToAny : StringTo<any>
+>nToAny : NumberTo<any>
+>sToAny : StringTo<any>
+
+    nToAny = bothToAny;
+>nToAny = bothToAny : StringTo<any> & NumberTo<any>
+>nToAny : NumberTo<any>
+>bothToAny : StringTo<any> & NumberTo<any>
+
+    nToAny = someObj;
+>nToAny = someObj : Obj
+>nToAny : NumberTo<any>
+>someObj : Obj
+
+    bothToAny = sToAny;
+>bothToAny = sToAny : StringTo<any>
+>bothToAny : StringTo<any> & NumberTo<any>
+>sToAny : StringTo<any>
+
+    bothToAny = nToAny;
+>bothToAny = nToAny : NumberTo<any>
+>bothToAny : StringTo<any> & NumberTo<any>
+>nToAny : NumberTo<any>
+
+    bothToAny = someObj;
+>bothToAny = someObj : Obj
+>bothToAny : StringTo<any> & NumberTo<any>
+>someObj : Obj
+
+    someObj = sToAny;
+>someObj = sToAny : StringTo<any>
+>someObj : Obj
+>sToAny : StringTo<any>
+
+    someObj = nToAny;
+>someObj = nToAny : NumberTo<any>
+>someObj : Obj
+>nToAny : NumberTo<any>
+
+    someObj = bothToAny;
+>someObj = bothToAny : StringTo<any> & NumberTo<any>
+>someObj : Obj
+>bothToAny : StringTo<any> & NumberTo<any>
+}
+
+type NumberToNumber = NumberTo<number>;
+>NumberToNumber : NumberToNumber
+
+interface StringToAnyNumberToNumber extends StringTo<any>, NumberToNumber {
+}
+
+function f3(sToAny: StringTo<any>, nToNumber: NumberToNumber, strToAnyNumToNum: StringToAnyNumberToNumber, someObj: Obj) {
+>f3 : (sToAny: StringTo<any>, nToNumber: NumberToNumber, strToAnyNumToNum: StringToAnyNumberToNumber, someObj: Obj) => void
+>sToAny : StringTo<any>
+>nToNumber : NumberToNumber
+>strToAnyNumToNum : StringToAnyNumberToNumber
+>someObj : Obj
+
+    sToAny = nToNumber;
+>sToAny = nToNumber : NumberToNumber
+>sToAny : StringTo<any>
+>nToNumber : NumberToNumber
+
+    sToAny = strToAnyNumToNum;
+>sToAny = strToAnyNumToNum : StringToAnyNumberToNumber
+>sToAny : StringTo<any>
+>strToAnyNumToNum : StringToAnyNumberToNumber
+
+    sToAny = someObj;
+>sToAny = someObj : Obj
+>sToAny : StringTo<any>
+>someObj : Obj
+
+    nToNumber = sToAny;
+>nToNumber = sToAny : StringTo<any>
+>nToNumber : NumberToNumber
+>sToAny : StringTo<any>
+
+    nToNumber = strToAnyNumToNum;
+>nToNumber = strToAnyNumToNum : StringToAnyNumberToNumber
+>nToNumber : NumberToNumber
+>strToAnyNumToNum : StringToAnyNumberToNumber
+
+    nToNumber = someObj;
+>nToNumber = someObj : Obj
+>nToNumber : NumberToNumber
+>someObj : Obj
+
+    strToAnyNumToNum = sToAny;
+>strToAnyNumToNum = sToAny : StringTo<any>
+>strToAnyNumToNum : StringToAnyNumberToNumber
+>sToAny : StringTo<any>
+
+    strToAnyNumToNum = nToNumber;
+>strToAnyNumToNum = nToNumber : NumberToNumber
+>strToAnyNumToNum : StringToAnyNumberToNumber
+>nToNumber : NumberToNumber
+
+    strToAnyNumToNum = someObj;
+>strToAnyNumToNum = someObj : Obj
+>strToAnyNumToNum : StringToAnyNumberToNumber
+>someObj : Obj
+
+    someObj = sToAny;
+>someObj = sToAny : StringTo<any>
+>someObj : Obj
+>sToAny : StringTo<any>
+
+    someObj = nToNumber;
+>someObj = nToNumber : NumberToNumber
+>someObj : Obj
+>nToNumber : NumberToNumber
+
+    someObj = someObj;
+>someObj = someObj : Obj
+>someObj : Obj
+>someObj : Obj
+}
diff --git a/tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts b/tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts
new file mode 100644
index 0000000000000..6eb9eca9657e5
--- /dev/null
+++ b/tests/cases/conformance/types/members/objectTypeWithStringAndNumberIndexSignatureToAny.ts
@@ -0,0 +1,95 @@
+// @strict: true
+
+// When checking compatibility between two types,
+// TypeScript should not require an index signature if
+// the target side index signature maps to `any` *and*
+// the target side has *any* string index signature to `any`.
+//
+// So an index signature like in
+//
+//  { [x: number]: any }
+//
+// is still required of a source type, but neither index signature in
+//
+//  { [x: number]: any, [x: string]: any; }
+//
+// should be required; *however*, the number index signature in
+//
+//  { [x: number]: number, [x: string]: any; }
+//
+// should always be required.
+
+interface StringTo<T> {
+    [x: string]: T;
+}
+
+interface NumberTo<T> {
+    [x: number]: T;
+}
+
+interface StringAndNumberTo<T> extends StringTo<T>, NumberTo<T> {
+}
+
+interface Obj {
+    hello: string;
+    world: number;
+}
+
+function f1(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringAndNumberTo<any>, someObj: Obj) {
+    sToAny = nToAny;
+    sToAny = bothToAny;
+    sToAny = someObj;
+
+    nToAny = sToAny;
+    nToAny = bothToAny;
+    nToAny = someObj;
+
+    bothToAny = sToAny;
+    bothToAny = nToAny;
+    bothToAny = someObj;
+
+    someObj = sToAny;
+    someObj = nToAny;
+    someObj = bothToAny;
+}
+
+function f2(sToAny: StringTo<any>, nToAny: NumberTo<any>, bothToAny: StringTo<any> & NumberTo<any>, someObj: Obj) {
+    sToAny = nToAny;
+    sToAny = bothToAny;
+    sToAny = someObj;
+
+    nToAny = sToAny;
+    nToAny = bothToAny;
+    nToAny = someObj;
+
+    bothToAny = sToAny;
+    bothToAny = nToAny;
+    bothToAny = someObj;
+
+    someObj = sToAny;
+    someObj = nToAny;
+    someObj = bothToAny;
+}
+
+type NumberToNumber = NumberTo<number>;
+
+interface StringToAnyNumberToNumber extends StringTo<any>, NumberToNumber {
+}
+
+function f3(sToAny: StringTo<any>, nToNumber: NumberToNumber, strToAnyNumToNum: StringToAnyNumberToNumber, someObj: Obj) {
+    sToAny = nToNumber;
+    sToAny = strToAnyNumToNum;
+    sToAny = someObj;
+
+    nToNumber = sToAny;
+    nToNumber = strToAnyNumToNum;
+    nToNumber = someObj;
+
+    strToAnyNumToNum = sToAny;
+    strToAnyNumToNum = nToNumber;
+    strToAnyNumToNum = someObj;
+
+    someObj = sToAny;
+    someObj = nToNumber;
+    someObj = someObj;
+}
\ No newline at end of file