Factions beyond Sigil

Most of the Factions are strongest on a plane that already mirrors their philosophy in some way, and therefore fits them like a glove. This was probably deliberately designed, especially on the law and chaos, so that Mechanus functions like a plane full of Guvners and Limbo like a plane full of Xaositects (over-generalizations obviously, but it does present familiarity).

The various Planes of __ boxsets did feature the sites where the factions were based or had particular influence.

The real issue is that Faction War, which more or less blew the factions apart, was one of the very last supplements released in the Planescape line, so there was very little material dealing with what the factions were doing post Faction War (and it largely took the fanbase well into 3e to get over the war having happened in the first place).

Most of the 3e material that has acknowledged Planescape at all has been very mechanics focused, so it's not very helpful.

Stories I ran in my own campaigns had the Factions very active in the Gate-Towns. Some were working very hard to prevent border shifts. I suppose some could be working hard to cause them, too.

For my home campaign's introduction to Planescape, the party ended up in PLague-Mort. Several facions were represented. The Bleak Cabal ran The Hospice, the safest place in town for a jinkless Clueless to sleep (which isn't saying much), if you can put up with the barmies and the Bleakers. The local Sensate was an artist who sometimes used organic media. He was actually out-ranked and knuckled under by one of the PCs. The Arch-lector's Hounds were split along Faction lines, with Dustmen, Doomguard, and Fated. The one high-up who ran them all was a chaotic-evil Cypher, who became another PC's nemesis.

The major part of the adventure involved the party working for a Godsman, Devi. She was a deva determined to prevent the town and its mortal residents from tumbling into the Abyss. The PCs had to run around town, planting flowers (yes), and helping specific people. This would anchor the town better to the Outlands.

The party also went to Bedlam twice (because I love creating odd and memorable NPCs). Again, the Factions were represented in various parts of town. The Dustmen ran the graveyard and the quarry (cheap manual labor), as well as a pawn shop (of sorts) of dead berks' property. The Fated were represented by a were-rat gangster who ran the cross-trade. The Sons-of-Mercy was a single bariaur paladin who thought he was the city guard. The Doomguard controlled the wall between the upper and lower towns, deciding who got to climb the hill and who stayed down by the gate to Pandemonium. The Godsman's local Factor was a Rakshasa who guarded the Temple to All Gods. There were even Guvners in the town, a family of gnomes who lived in a large stout bulding that was always locked (the 'bank').

This was all in addition to the Factions that really ran the town, the Xaositects and the Bleak Cabal.