While the fundamental "team style" of mafia, (small but ordered/strong team of mafia vs. large but chaotic/weak team of town) is cool, I think we could grow some alternatives.
Like, imagine this as an alternative: There's Rocks, Papers, Scissors and then the usual neutrals. The Rocks want to kill all the Papers and be left with only scissors alive to win, Papers need to kill scissors and keep a rock alive to win, and so on.
Admittedly, the logic may make your head hurt when you first think about it, but wouldn't this make for some really interesting interactions? Like a Rock trying to kill a scissor, but the scissor not wanting to fight back in self defence because he doesn't want to reduce the number of Rocks. Or a lack of Papers resulting in the Papers temporarily making a truce with the Scissors they plan to kill so that they can work together to stop the Rocks killing all of the remaining Papers. You may even, as a Rock, backstab a fellow Rock that's doing more harm than good! While it may not seem intuitive to kill someone who's theoretically working towards the same objective as you, you only need one Rock and many scissors for the Rocks to have an ensured victory.
Now, there's some blindingly obvious issues with this - trials wouldn't really work so well in their usual state, the mass killing we're used to in mafia would probably suck even more in this "alternate team style", but, with creative, rational theory crafting, I think this has the potential to be a pretty cool idea, if it is built up by multiple minds. I was thinking that the game would be focused on an economic system instead, with the buying of gadgets and income being the main thing that advances the game, rather than loads of deaths over the course of the game. Most deaths would take place towards the end when people can safely afford it.