How to extend an interface but limit the keys to a specific list

In typescript, how can I extend an existing interface but limit the use to the same keys?

Existing interface:

interface First {
  key1: string;
  key2: string;
}

interface Second extends First {
  key1: number;
  key3: string <<< this must be prevented and generate error!
}

The example is intentionally reduced to understand the topic, obviously the application is for much more complex interfaces.

In all the tests I've done, when I extend an interface I can always add any kind of new key.

You can just override :

type Override<T, U extends { [K in keyof T]?: any }> = {
  [K in keyof T]: T[K] extends U[K] ? T[K] : U[K]
}

interface First {
  key1: string;
  key2: string;
}

interface Second extends First {
  key1: number;
  key3: string
}

type Third = Override<First, {key1:number}>

var myOverride:Third = {
  key1: 5,
  key2: 'six'
}