Allow extending multiple interfaces with different, but compatible types

interface Change {
  uid: string;
  type: string;
}

interface SomeChangeExtension {
  type: 'some';
  foo: number;
}

interface SomeChange extends Change, SomeChangeExtension { }

In this example, I was expecting SomeChange to have a type equivalent to:

interface SomeChange {
  uid: string;
  type: 'some';
  foo: number;
}

But it would result in error:

Interface 'SomeChange' cannot simultaneously extend types 'Change' and 'SomeChangeExtension'.
  Named property 'type' of types 'Change' and 'SomeChangeExtension' are not identical.

In this case, 'some' is compatible with string if the order of interfaces being extended is respected.

The reason why I want this to be allowed is that, I need to maintain multiple interfaces of the same kind of change during different stages: raw change, change, broadcast change. And having to duplicate part of the "extension" on every of them doesn't look good.

Start by reproducing the interface example in the TypeScript compiler and inspect how multiple interface extensions check members with the same name. Done means compatible narrower properties such as 'some' and string are accepted while incompatible declarations remain errors; no specific files or tests are named in the issue.