Oh, ours fight too!! We have approx 24 birds right now. Sometime while fighting they have slammed into our glass doors and really stun themselves.
We hang 4 feeders to try and keep them pacified.
here's one that "beaned" himself on the glass door. He lay in the towel we put him in for almost 45 minutes...we were starting to think he wasn't going to make it...them out he came. :D