Most of the Rattrap games we have done as a gaming group have been done with up to 6 players. .45 Adventure, Fantastic Worlds...still no Gloire(will work on that, Pete!) and I have run convention games with 4 players for Broadsword Adventures.
Just make sure that you have a good story backing things up and it goes well. Make sure that there is a good "reason" for all of the teams involved to be involved. Also, if there is one central sort of Maguffin, the sought after thing, make sure that not every faction wants it for the same reason.
The BA multi-player game I ran most recently had a faction looking for an escaped slave girl and another faction of escaped slaves looking to find her and escape with her. You have instant tension between the players for the slaves and escapees that centers not only around the objective. The third faction was looking for black lotus in the jungle and if they found the slave girl, could have made use of her for big sorcery purposes as a sacrifice. The fourth faction consisted of natives looking to drive away the interlopers. With that kind of dynamic, it was a fairly simple game with many different outcomes each of the times it was played out.
Be sure you have enough encounter markers and enough diversity in encounters to keep things interesting for the players. Some encounters might mean nothing to one team while might be very important to others. For that game I had two kinds of encounters for the players to explore, totalling up to 24 encounters. Many were essentially nothing, some were "traps" some were helpful things and, of course, the goal encounters. Try to have those be triggered by more than one encounter--meaning you have to find two encounters before the "goal" can be found/recovered. This keeps you from setting things up only to have the goal encounter be located on turn two.
In speaking of turns, I have used a card based initiative system and found it to work quite well. Each faction has a card and each model has a card as well. These are shuffled together and drawn out at random for activation. That way, you know your entire team will activate together once per turn and then individually as well.
I try to limit grades to no more than 5 total for games, as more than this can bog things down very quickly.
Hope my suggestions are usefull.
Ryan