Planescape: Across the Multiverse
While less influential on the outer planes (and barely caring about the prime), the factions run Sigil. Actions the characters perform can change their standing with the different factions, and faction membership itself is a major factor. Joining or performing work for the Fraternity of Order isn’t going to win you any friends with the Xaoseticts. Making enemies of a faction can lead to trouble with the people and services that Faction influences; on the flip side of that, staying to close to a particular faction may mean that other factions won’t offer jobs or services.