In any event, I was hit with the idea of concurrence; objects occupying the same space in multiple universes. This is easy to detect by checking the coordinates of objects in each universe.
What to do with concurrence? Well, one option is to limit travel between universes to concurrences. This enables some interesting options for the players. If someone managed to locate a concurrence on a world, they could conceivably create a "pocket" empire. Or, perhaps the resources on the alternate concurrent world are better than on the current world.
How do you model concurrency? This image (hastily made in Sketchup) is probably the best way to illustrate the concept:
Point A has concurrence with Point D
Points B and C do not have concurrence with anything.
Now the question becomes, at what level do we have concurrences? The above example is at the system level (each square = one square light year). More likely doing it at the celestial level (planets, asteroids, etc) would be best, but much less likely