I think it needs to be said though that most empires are formed by invasion. stealing countries, in other words (through the the cunning use of flags ^_^)
In my view,Empires generally work by forcefully stamping over your culture, your view, your way of life over the cultures of the people you've conquered. Romans are a good example of this. This is part of the reason why so many Empires in real life don't last very long, you can only opress people for so long before they cracked.
That said, though, if they do find some commonalities like you said, the Empire can work. China is a good example. The dynasties may change but the essential cultural identity does not change since the Qin Dynasty.
Anyway, this is just my view. Ignore it if you think it's crap.