It does indeed sound a lot like the European Union, and not by accident. But actually it makes more sense to compare the Union to the Holy Roman Empire than to Byzantinium as in contrast to the later, they both lack an imperial center, a metropolis like Rome for the Roman Empire or Constantinople for Byzantinium, but are federal political structures. A comparison that has actually been made in the political science, for example by Jan Zielonka (Europe as Empire. The Nature of the Enlarged European Union). For some reason I cannot comment on the article ... ("please specify a valid author)