I just got an idea (hooray for me!)
Okay, here it is. As the subject suggests, their would be a couple facilities that would count for the entire empire, just like the system wide facilities. (Only one would work at a time, but instead of one for each system, one for each empire)
Examples:
Emperor's Palace: Would give small bonus to happiness, production, etc. Cost quite a bit of money to build.
Main Intel Center (for lack of a better term): The main facility for all intelligence ops. All operatives report to the main center.
Main Research Center: The research coordination center, a really really big computer maybe.
Also, we'd have to add a few for the special techs, I dont know what though.
Others?