Their own faction?
Personally, I don't think that'd work. Why were the characters on their own in the first place? They didn't like where they came from, obviously, and they didn't want to be controlled by someone else, more or less. And in the times that the roleplay takes place, starting one's own 'faction' would be difficult, since you first must make a name for yourself in some form or another, and then gain peoples' trust, and gain something to keep them in- land? money? items? Expensive and lengthy, to make one's own faction. One would worry if it were some guy starting a rebellion, or simply trying to single you out so he can slit your throat and take your coinpurse.