Any one remember the factions presented by Tim Beach? I believe that they were supposed to have existed in Sigil at an earlier time, but had fallen into extinction. Of course, in a place deeply entrenced in belief, anything can be brought back into existence.
From my notes, I have the The Beautification League (the Decorators), The Free Flora Collective (The Veggies, the Tree-Huggers League), The Herbivorous Assembly (the Vegetarians), The Wizards of the Black Teddy (The Babes), & The Apathetic Alliance (the Apathetics).
I believe they were featured in an April Fool's edition of Dragon. Aside from a casual chuckle, would anyone really allow such a faction to operate?
Me, I'm fairly happy with the original set of factions and have seen no reason to expand upon that number. However, it is stated in a few places that there are factions outside the City of Doors, which never got a foothold in Sigil itself. Such "factions" would receive little serious attention from most Cagers, but might have a plane wherein their philosophies are widely aknowledged.