Merge two groups

My site has the following two kinds of group types:
1. Matches, where a limited number of users are allowed to join. Members are allocated in two user roles that will play against each other.
2. Teams, where users can chat between friends.

What I'm actually trying to do is to create a third type of group, the Team Match, where two Teams Groups can challenge each other. This group would allocate the members of both groups in different roles, in order to allow me to configure a nice "view" page. (btw, anyone knows if I can separate the members in two "teams" on an easier way?)

I'm actually using Organic Groups because of the flexibility it provides me. I've already tried several other modules like the Tournament and the League Module, but they don't fill my expectations at all.

Would you know some module extension for Organic Groups that I can use in that case?