Just be sure you actually have a fight before you start taking names.
Several years ago, we had a game where the visiting QB threw a long interception (downed inside the 10 yard line). The home crowd began to cheer (and maybe jeer), so the QB invited the whole home crowd out onto the field to address the situation. The home bench emptied, which resulted in the visiting team bench emptying, and I looked up to see the Lineman furiously writing down numbers.
I asked him what he was doing, and he said he was getting the numbers of all the players that left the bench. (Frankly, it would have been easier to write down the numbers of the players that DID NOT leave the bench.) I told him that no punches had yet been thrown and he looked a little confused. We went to the Ref and the L begins to tell him that he has all these players that had left the bench and the Ref looks like he's going to be sick because he's going to have to eject half or more of each team. I pointed out to him that no punch had ever been thrown, and a look of relief came over his face. Everyone had just got into one another's faces and jawed, but no one ever threw a punch, just verbal insults.
We wound up with USC on each team and went about the rest of the game with all of the players still participating. Would have hated to write that game report!
Also, I've never heard of this sanction against a team for any number of ejections during the season here in Alabama. A player can be benched for multiple ejections during the season, but I don't know of it going against the whole team.