So, I have yet to play this game (just ordered it now), but I'm a big fan of MP MtG games. I've played many variables, and I believe most can be adapted to this game (actually I'm counting on it, I want to use this as a sort of "many players party game" because everyone got tired of sinking money into MtG).
The biggest drawback of this game when playing with more than 2 players is the extended playtime, but there are a few workarounds I can think of.
For 2v2 or 3v3, I think the most important rule would be the whole team plays at the same time (with the initiative). This would make so the game doesn't extend much beyond the normal game time. It can sound confusing 2 or 3 players playing in tandem, but it's actually more practical instead of each player having a turn. This is used in two headed giant games in MtG (specially the console spin offs) and it speeds things up noticeably.
Another optional rule would be, shared life. This is also used in 2HG, and it is a great way to speed things up as there is less stuff to keep track of, there is less reason to turn 1 gang up on someone (which otherwise would remove the player from game, and dictate early the winning team), and everyone keeps having fun until the end of the game. Life would need to find a sweet spot. In 2HG I usually use number of heads of the giant times 15 (75% of regular health). A direct adaptation would be adding the HP totals, and multiplying by 75%. Again this would probably need to be tweaked.
Another MtG variant, Emperor, has the teams trying to kill the opposing team Emperor (an otherwise regular player in this case). This would potentially speed up the game, because it would end when the emperor was dead. Each player would have individual health in this case.
Then we can have the 1 v many games. This works best with carefully made decks obviously. 1 player is the all powerful mage, with more HP, more mana, more deck building points, initiative, maybe even more cards in hand, and everyone else is a lowly mage trying to kill this big boss. This one I'll elaborate better when someone tries it and tweaks it on the game...