Here's a fun little variant that is also a great way to introduce new players to the game.

Take that stack of extra commons and uncommons you have, put it in the centre of the table and start playing.

All of the rules of VS are already set up to make this work. The Player with Init draws their 2, then everyone else in order.

The only real change is that everyone shares a single KO'd pile. This adds some strategy as you can knock out an opponent's card and then recover it for your side.

I've played this way a few times at it works fine. Sure, the results are kind of random and there are a number of team specific cards that are almost useless, but surprisingly its not THAT much more random than Sealed Deck...

There is a MTG variant just like this, except the decks are, I think 500 cards and are constructed, and four players play off of the same deck. I like this idea. Have fun shuffling!