How to cast an Iterator of a class to an Iterator of a subclass thereof?

I tried to cast an Iterator of a class to an iterator of a subclass of said class. This gave me an "inconvertible types" error. Why is this not possible and what is the most elegant way to work around it? (Or alternatively, why is it a bad idea if it is?)

Using a for-each loop is not a solution in this case: I'm trying to implement iterator() and the easiest way to do this would be to return the iterator() of one of my class' fields, but that one doesn't have the exact required type. I can't change the signature of my iterator()either.

public interface SomeoneElsesInterface {
    public Iterator<SomeoneElsesInterface> iterator();
}

public abstract class MyAbstractClass implements SomeoneElsesInterface {
    final MyAbstractClass[] things;
    public MyAbstractClass(SomeoneElsesInterface... things) {
         this.things = (MyAbstractClass[]) things;
    }
}

public class MyClass extends MyAbstractClass {
    public MyClass(MyAbstractClass thing1, MyAbstractClass thing2) {
        super(thing1, thing2);
    }

    public Iterator<SomeoneElsesInterface>() {
        return (Iterator<SomeoneElsesInterface>) Arrays.asList(things).iterator();
    }
}

I could, of course, just change the type of things. However, I would need a lot of casts in other places in that case. I do know that my constructor won't be called with objects that are not MyAbstractClasss but I cannot change the interface anyway.