How to extend an apex set class?

 Is there any way I can extend the Set class? I have numerous places in code where if a set has no items, I want to add all the items in another set, but if it does have items, I want to retain only the items in the other set.

This seemed like a good use case for extending the Set class, but Apex complains about the lack of < following>

public with sharing class CoreSet extends Set {
    public Boolean retainAllIfPopulated(Set other) {
        return this.size() > 0 ? this.retainAll(other)
                               : this.addAll(other);
    }
}

Is it possible to extend the built-in Set class?