interface Base {
   foo: { [key: string]: any };
   bar: any;
   baz: any;
}

interface E1<T> extends Base {
  foo: T;
}

interface Something { name: string, value: string };
interface E2 extends Base {
  foo: Partial<Something>;  // or other mapped type
}

interface E3<T> extends Base {
  foo: Partial<T>; // or other mapped type
}