I've heard a lot of things over the years about BJJ not being any good for multiple opponent situations, etc., and for the most part I agree. This goes back several years before the first UFC (1993) when everybody "else" finally heard about it and wanted to learn it.
One thing you have to understand is this. In terms of handling multiple unarmed opponents, the BEST person to handle this is a good grappler who can box. Boxing alone is not as good, since multiple opponents tend to grab, crowd you, control, and hit. They don't all just stand at range and tee off.
Secondly. I've trained in boxing, kickboxing, traditional Asian punching and kicking arts, Filipino martial arts, wrestling, and submission grappling for about two decades. The most advantageous position in all of fighting to have your opponent in (barring none) is the knee on chest position. It's the fish in a barrel position. If I were fighting two game opponents (guys that just don't go down from the first good punch), I'd want one of them on his back under my knee where I could REALLY hurt him. Yet, in this position I am standing, mind you. One person is completely incapacitated, where I can knock him out in about one second (equals 5 to 7 solid punches on the chin which WILL NOT miss because he can't move or defend). I would turn to where the other guy is in front of me, do in his friend, and the guy that's still standing can't get to me in time without stepping on his own friend. To go around, he uses up that precious second I just used to knock out his body, and now it's his turn.
I'm already standing when in a high knee on chest, and I can stay low and take the other guy down, grab his kick if he tries that and take him down, or go right back to stand-up fighting, now mano a mano.
This is a scenario I've practiced, taught, and applied for many years now, and anybody skilled in BJJ will have this going for him. It's one of the best ways to deal with two opponents -- i.e. where one of them is completely unable to hit you, and the other is not able to get to you in time. As I said before, the guy on his back is knocked out in a second or so, and you never went to the ground. Even an intermediate takedown artist can put a larger opponent on his back and kneel on his chest, post the other leg 45 degrees off the shoulder, and shoot the fish in the barrel.
If the standing opponent is behind you, then you switch to the other side around the head (takes about 1/3 second), OR you abandon the position altogether and take your standing man out. You have about 2-3 seconds to do it before your knee-on-chest guy gets back to his feet -- an eternity compared to the amount of time you'd have if he had never been on his back.
I generally chuckle to myself when I see some of the assumptions people make about arts they haven't trained in, but enough is truly enough. I'm considered a pretty fast heavyweight as a boxer, and even I'd prefer to put one of my two opponents on his back to knock him out. This comes from having had to deal with both opponents standing in the past, and knowing certain dynamics that make this difficult.
P.S. And if you need to run away, knee on chest allows for this as well. Like I've said before, ground grappling does not necessarily mean YOU go to the ground -- only that HE does.