I have nowhere near enough experience to properly run such a thing, but I feel there needs to be a pro wrestling rtd . Players would be the wrestlers, of course and everything would be kayfabe (which means we act like it's all real), so anyone with powers actually has powers (although, from what I know of the genre, these tend not be reality-altering; rather, they're more often just very useful tricks). Players would decide how many points they want to spend towards being either a heavy-hitter, a speedster, a trickster, or some combination of three (or possibly more, but I can't think of any others right now) and pick or maybe build their moves.
So, anyway, the basic idea is that you'd have some players competing in matches with each other, probably there'd b several matches going on at once so more happens on a turn, and then anyone who isn't currently participating in a match engages in backstage drama (which entails things like insulting each other, picking fights, creating alliances, bringing up dirty secrets, etc.) or can try to interfere with an on-going match.
Now, I'm not sure how long matches themselves should last. They should be long enough that players have time to execute all their cool moves and people can interfere with a match without influencing it too much, but not so long that they drag on and there isn't much opportunity to fight a lot of different opponents. Also, I'd like the game to support fatigue, which prevents one from easily partaking in multiple matches in a short order of time and defending against attacks outside of the ring when tired, and injuries, which negatively impact one's performance in the ring and can be exploited or exasperated by certain attacks and take time to heal. Though, I suppose, if matches don't run too much longer or shorter than each other, the time between them can be skipped ahead.
While writing this, I realized this idea could alternatively be retooled as a worldwide fighting tournament. Actually, it might even work better. You'd just have to get rid of fatigue and make matches fights to the death or just defeat leading to banishment from the tournament (maybe the winner could decide the loser's fate, so long as other players are able to try to intervene in any impromptu executions).
Either way, the focus of the game should not be solely on the fighting, but also the drama behind the fighting. Players should be encouraged to come up with backstory that links them to other players, giving more meaning to grudges and alliances. If possible, the match-up system should make it more likely that players get to fight someone they are currently feuding with.