Follow up thought: it would be cool if you imagine a match to consist of three sets each for a different class.

So each player comes with three teams of small, mid and large base stat classes. You can't repeat monster across teams. Whoever wins 2/3 wins the match.

...

And if this was my college house, we would have a price system for the mons so you wouldn't be able to repeat mons even between players. But that's a different thing altogether.