It is technically possible to use Facebook Connect on multiple domains, there are some limits (5 domains max).
So the key to doing this is adding all domains in the App Domain field under your app settings.
The PROBLEM, however, is that Facebook only lets you add domains that are derived from your Canvas URL or Site or Page tag URLs, so if you try to enter anything else you get an error that looks like this:
The SOLUTION is to create App on Facebook, Website, and Facebook Tab using the ADD PLATFORM button and then put in URLs that point to your other domains. Here is an example of what I mean:
If you use a unique domain for each field you can max out with 5 different domains. I have tested this technique with up to 3 domains, but i think it should work for all 5.
Note: Facebook admin features change from time to time, so all of this is subject to change