foo.ts

class ThingFactory {
  constructor(private readonly service1: Service1, private readonly service2: Service2) {}

  make<T extends OtherThing_1 | OtherThing_2>(arg: T) { // no need to declare return value. If you want to, it's T
    // use this.service1 and this.service2 here
    return arg;
  }
}
    
const factory = new ThingFactory(service1, service2);
    
const thing = factory.make(new OtherThing_1()); // type of thing is OtherThing_1