Would be possible for Compiz to work on Windows?

Question

I obviously don't think it would work as it is. Its more like, does Windows internal architecture allows for some third party SW to integrate in between? From what I read about Compiz, I believe it creates its own window, and somehow mixes graphics from System X to its own. But it still has to catch events like EXIT button and so on.

Does Windows even allow this? Let 3rd program to scan for input of another window? And more, catching output of GUI and replace it?