Well I'm glad to say that we all support one another at my school. Its common to see us attend events sponsored by other orgs (There are 6 orgs represented on campus).
I think its also good when GDIs see our interaction. It gives them a more positive picture of greek life and they see that just because you want to join one organization doesn't mean you can't hang out with members of another.
Basically we are all striving for the same things. We should work together on a local and national level more often.