What do the factions look like, assuming the module-which-must-not-be-named never happens?
The fifteen factions published are just a snapshot in Sigil's long history, and I imagine it to be a snapshot of a brief and unstable time, even without the Faction War. Some of the factions don't look viable for any great length of years, while there's at least one obvious 'job opening' for some new faction to fill:
The Athars' 'job' in Sigil is to keep an eye on the temples, and make sure none of them get too uppity and powerful. Isn't it odd that there's no faction to keep an eye on the mages to make sure there isn't a repeat of the Incantifer incident? (Not that the Lady couldn't maze another faction of overreaching mages, but the purpose of the factions is her not having to micro-manage things.)
On the other hand, there are a couple of factions with awfully similar philosophies. If the Xaositects were subsumed by the Bleak Cabal and became a sect of said faction, would anyone notice? Both factions essentially say "There is no order or purpose to it all." The chief difference seems to be "...so find your own meaning" vs. "omg crzy funzy xaos is lol!" ('Cause you know if Sigil had cell phones, Xaositects would be the masters of incomprehensible text-speak. 
)
Similarly, if the Mercykillers were subsumed by the Harmonium, would anyone be surprised? Some might call it a shame if Sigil didn't have its Trifecta of Lawful Factions to demonstrate the Rule of Three. But I'm sure there's a more distinct philosophy out there suited to running Sigil's prison.
Finally, there are a few factions that just don't seem like they can make the long haul. Their philosophies are weak, and their emotional appeal is limited to very small percentages of the population. The Doomguard might survive as a crazy fringe group of...the Bleak Cabal maybe? All the Dustmen will probably eventually 'ascend' to undeath, or...grow out of their black nail polish, their many body piercings, and their goth rock, I guess. (I kid, I kid. Sort of.) And the Revolutionary League...well, I guess anarchism will never truly die in a place like Sigil. But really, are a few extremists without a real philosophy enough to call a Faction? (Even by us, Sigil's omniscient-perspective viewer?)
So, opinions? Ideas? I remember seeing an on-site list of lore, including fan made factions, but I can't seem to find it. I'm thinking of actually following thru with these lines of thought for my own campaign, so I'd appreciate pointers.
Well, I played in the module-which-must-not-be-named and in our version the factions didn't have to leave. IMO going that far in the future kills most of the NPC's, a problem even bigger than the 4th edition FR. Might as well throw out the old books about Sigil. Like you, once I did consider changing the factions, but now I think most other philosophies can exist within them.
Some factions do appear too extreme to attract large number of people, but I think they started based the influence of particular outer planes, the Anarchists appeared as a reaction to the oppression in Carceri, or Baator. Xaositects exist cause the force of Chaos is real in the planes, it has a purpose, different than the Bleakers. I see more similarities between the Indeps and the Bleak Cabal. The Destroyers fraction of the Doomguard is popular cause their overt show of destructive power, but it's the Regulators that gain real influence after the Destroyers pass. Same symbiotic relationship is in the Mercykillers, makes sense, both would lose a lot of influence without each other. Post-Faction War groups make less sense to me, the Ring-Givers should be a sect.
Concerning fan made factions, I usually have five additional, so it's a d20 roll. One of them is Teknists, they are opposite to the Incanterium on the technology-magic axis. Mentioned in this thread /forum/additional-sects-or-factions