The only thing with group claims is that you would have to have a good number of the group in the fic with more than just a "oh hey there's so-and-so sitting over there." I would say you have to have least half of the group in the fic in an active role.

For a group/group interaction claim, you would probably be better off taking a general series claim. Then again, if each group consists of three characters (so we're looking at 3 characters interacting with 3 other characters) that would probably be okay.

The general series claim does not mean that each of your fics has to be gen in nature, but it allows you to play around with all of the characters instead of just one or two.

I hope that answers your question.