I always akin Crossgate to Cynosure. The city from the old, sadly defunct, Grimjack comic.
Basically dimensions meet at random points in the city. I'll describe how it worked with an example.
Lets say one morning you walk out of your house and across the street, instead of your neighbors house you see what looks like an old medieval tavern. Interested you walk down the street. Suddenly you walk in what looks like a bee hive. Walking further down, it looks like buildings from a utopian future city. You, and more likely the area of earth where your house and probably a few square miles of land have been "phased in" to Cynosure. You walk | run back home and when you get there. Nothing. Your Neighborhood has been "phased out" back to earth and, because you weren't there at the time, you are now trapped in the city.
Also in Grimjack, some parts of the city where so Phased In that you could walk right into there attached dimensions. Other times dimensions phased in and out long enough to develop a few "squaters".
Least this is my picture of crossgate and something I'd like to use as a basis when the new scripting engine comes out.
Course the city could be something closer to Wormwood or Sigil or hell even stargate. In that case, your idea pans out more.