3 vs 3 tag style
 

Is there anything else besides the ultra rare/never gonna happen Marvel vs Capcom 2? Or some really awesome 2 vs 2 that is easily found/downloaded?

It's not a fighting game, but Warriors Orochi has tag team mechanics as far as the players are concerned. NPCs are a different story.

Warriors Orochi: Rise of the Serpent King will have a vs mode.

Look into MUGEN. Don't know if it has 4+ multiplayer but it's hugely customizable. Search it on YouTube.

MUGEN is terrible. An unbalanced joke.

Recent KoF games have had Tag Modes.

If I were you, I'd just keep checking gamestop.com periodically for a used copy of MvC2. Probably gonna run you around $100, but the game is ridiculously rare.

King of fighters XI is 3 on 3 tag. You can probably find it on the ps2 for like $15.