In such a scenario, it would be natural to have Germany, Italy and Russia besides Byzantium. Add England and USA that grants room for one more. Say this is set in 1940-41, after the fall of France?
Also, which would be the natural allies of Byzantine? Would it support the formation of a Third Reich and Mussolini's dream of a new Roman Empire, or would it be opposed to this? Especially since Mussolini might view Byzantine as a possible conquest? Perhaps it would be best to let the player decide which side he sides with, or if he doesn't side with either and tries to fight the war on his own?
As a part of the Axis the Byzantine fights against Russia. One could argue that one Orthodox nation would be a natural ally of another Orthodox nation, but on the other hand, Communism in Russia suppressed the church, and allying with Germany could be seen as an attempt to free the Orthodox church from Stalinism.
I doubt any Christian Byzantine Emperor/Empress would support Hitler, though I could be wrong. Would Byzantine make another Axis or another Ally?