I'm not bagging MMA, but some decent weapons skills (defending against and disarming) and learning to cope with multiple opponents would be quintessential to participating in a street fight. As far as I know MMA doesn't give you any tutelage for this because it is a sport but any good self-defense school would.
Don't get me wrong, someone who practices MMA would have the advantage in a punch up since you are trained to take and deliver punishment but as soon as weapons or multiple opponents are involved (typical in a street fight) it becomes a whole new ball game.