Let me start off with my preferances in MP games. Avoids King of the Hill ie lets kill him because he is close to winning, avoids kingmaker rules ie I can't win but I can choose who wins. Avoids stealing kills ie I killed all the defenders and player after me burns the now undefended zone.
I'm thinking a multiplayer system like Vampire ccg (V:TES) would be simple to play. The player to your left is your prey and the player to your right is your predator. Players would be able to only attack their prey from the battlefield, but they could use tactics or actions on anyone. You get a victory point whenever the player who is your prey is ousted (no matter how or by whom your prey was ousted). You receive an additional victory point if you are the last player left. At the end of the game, the winner is the player with the most victory points, even if she has been ousted. Along with a victory point, may you remove 4 damage from your capital or put into play 4 developments from the top of your deck when your prey is ousted.
Two headed giant. You and your partner share the exact same zones. Each zone has a total of 16 life. With the exception of zones and zone life total, a team's resources (cards in hand, resources, and so on) are not shared. So if my teammate places a one power unit in the quest zone and I do no have any units or support cards in the quest zone, I do not draw 2 cards on the start of next turn, but my teammate does. Teammates may review each other's hands and discuss strategies at any time. Each team takes turns rather than each player. Both the players on a team take their team turn at the exact same time. Thus the players share phases as well
All ears for more suggestion and ideas or thoughts about my suggestions.