How bout in a Doubles or Triples games, after all the teams are eliminated except the winning team, instead of the game ending, teammates start attacking eachother. Then instead of points being divided equally, they can be divided by order of finish. In a triples game, whoever finishes 1st on the winning team gets half the pts, 2nd place gets two thirds of the other half, and 3rd place gets the rest. In a Doubles game, whoever wins gets two thirds, while 2nd place gets the other third. This would add whole new strategys to the game. Doesn't have to be permanent for team games either. Could be a game option, and be called Doubles/Triples Cutthroat or something.
I personally wouldn't play this type of game. In a team game, sometimes in order to win you have to dump all your armies on your teammate so they can fight the good fight... doing so would give them a horrible advantage in the "cutthroat" portion of the game. It would suck to ask for some help in game and have your teammater respond "No can do, I don't want you stronger than me when we win."
Any interesting game option not high on the priority list but something that could be interesting down the line.
"The suitcoats say, 'There is money to be made.'
They get so excited, nothing gets in their way
My road it may be lonely just because it's not paved.
It's good for drifting, drifting away."
-Vedder