I'm trying to think of both edition-neutral mechanics (or really just 3e and up) and story possibilities for having PCs run a small part of Sigil. This could be any part whether it's a community in Undersigil, a ghetto in the Hive or a wealthy neighbourhood in the Lady's Ward. It's something I thought of since I'm playing through the Kingmaker adventure path, but it's not something I want as complex as that adventure paths rules on nation-building.
This could be like having a Stronghold, and there should be roughly equal in different ways benefits of having a part of the Hive or the Lady's Ward. I want something where there's a focus on what types of buildings and people in an area, and what sort of benefits, liabilities, story hooks and game mechanics stuff it might bring to a party. Based on the ward of Sigil, the concept of how the party "runs" a neighbourhood could also vary. Portals are also something that probably should factor into this.
If you don't want complex rules, then stick to a few basic concerns, which related adventures would address:
1.) Why do you want it? If it's just power or money, you're going to have trouble convincing the locals -- or anyone else -- to help you get it. Do you want to eliminate a rival? Do you want to bring the locals the Truth? Do you want to just clean up a bit of Sigil and help some people live better lives? In any of these cases there will probably be people whose interests align with yours. This will also inform the shape of the organization you'll be trying to set up (for instance, how hands-on do you want to be?).
2.) You will have competitors as you try to set up. How will you deal with them? There may be previous powers in the region or rivals for the current position. Sigil's legitimate government will expect its due out of your territory, in taxes and in keeping the locals law-abiding. Flout those concerns and you'll have the law as an enemy, which means something anywhere except the Hive. You had also better be on the right side of the dabus and the Lady, which should limit your ambitions, admittedly at the high end. You'll also have locals who object to you personally, Anarchists who don't like anyone taking control, and monsters or other hazards that will be a threat to newcomers.
3.) Once you've got control, then it's a matter of keeping it -- from incoming usurpers, to challengers from inside your organization, to random Sigilian threats and changes in conditions. One way or the other you'll have to be acquiring resources, and that's going to mean some kind of donations if the neighbors are willing, or regular fees if the enterprise is more mercantile and you're providing a service businessmen and the wealthy are willing to pay for, or extortion and crime if you're just a gang leader. (Although even these guys may "earn" tribute and bribes if they are sufficiently powerful.)
4.) And what are you spending these resources on, other than maintaining your rule? If your rule has some kind of a purpose, like advancing the neighborhood's interests or cementing a faction's control, you will be needing to work on that. Failure will start deligitimizing you, whatever post you have. If you're supposed to be in the business of advancing the locals' political interests, you will need to be able to bring back good news from the Hall of Speakers regularly enough to prove your worth.