Some portals in Sigil (and other places) do not necessarily lead to other planes or worlds or other parts of the city, but to privately owned and designed dimensions. The most numerous of these falls into the category of 'living space'. Because of the shortage of living space in Sigil, many magically gifted denizens have resorted to hiring a tiny space and expanding it with the help of pocket dimensions. These dimensions are sometimes even hired out. Sometimes, one door opens multiple pocket 'living dimensions' with different keys.
Other personal dimensions include government offices, legal and illegal storage facilities, illegal breweries, 'smelly' industries such as tanneries that are safely tucked away in other dimensions, music rehersal spaces, brothels, personal parks/zoos, secret laboratories and prisons. Portals are frequently ordinary doors, large mirrors, door mats and walls. Keys are often ordinary room keys, but can theoretically be any object (or even thought)!
PCs might find or might be sold a key to one such dimension. They could also end up in a personal dimension by accident or have the mission to free someone from one.