I can sympathize.
One of mine generally starts it. My moody child..
I don't intervene usually ... unless they just keep nit picking on the others because I don't think kids should have to put up with that. It's like critiquing what they are doing .. like "stop doing that so loudly..." and I'm like "Ok, out you go till you can be decent to people."
My feeling has always been, if they treat people like that in the real world (school, later on at work, etc.) people will drop them as friends, so they have to not be included for a while.
If two or more kids are fighting, then I separate them. Or throw them all outside. It is usually from boredom I find, or we need a friend(s) over to change dynamic, or send them off to friends - or take them all to park or something .. just divide them up.
But for the most part, I let them deal with it. It's taught my younger ones to be toughies (usually the older ones start it).