I honestly don't get the question Byzantium vs Greece. Byzantium was the shattered remains of Rome. It was an Imperial nation that once aggregated the greek-speaking peoples in the East. Greek-speaking because it was both the cultured language and the "lingua franca" of trade. Not culturally Greek. We are not in the Low Middle Ages timeframe in which one could argue Alexandria, Antioch and the like were Greek cities.
By the 15th century
Greece (or Hellas) could be a formable nation with Achaea, Morea and Athens as suggested above. Cores in Larissa, Thessalia, Macedonia, Edirne, Naxos, Corfu, Thrace, Crete. Maybe (just maybe) in the shores of Asia Minor too.
Byzantium would still be the Imperialistic nation that would strive to dominate the whole of the Eastern Mediterranean as it once did: Greece, Macedonia, Thracia, Dacia, Southern Italy, Illyria, Asia Minor, Trebizond, Armenia. And then Syria and Egypt. And then Mesopotamia, Africa, Mauritania...
Why can't they both be possibilities? It'd be the same as saying you couldn't form Ireland, because their lands are part of what would became the United Kingdom in 1801.
I'd like to see Greece and
Ireland as suggested above.
Hispania (Portugal+Castille+Aragon): It almost happened as there was an heir to the three kingdoms recognized by the Estates of them all:
Infante Miguel of Portugal (1498-1500). His mother (the heiress of Castille and Aragon) died in childbirth and the child died aged two. And then, for something completely different: the Habsburgs inherited. Business as usual
Italia was an old dream, although it only came to pass in the XIX century: hope it's in too.
I think someone also suggested Burgundy. Or
Lotharingia: something that expresses the ambition of the Dukes to get a crown of their own.
At the beginning of the XVI century the Jagiellonian dynasty ruled Lithuania, Poland, Hungary and Bohemia. They were not all under a PU because Casimir IV willed that his eldest (already King of Bohemia and Hungary through is mother), would not inherit Poland and Lithuania also, that passed to the younger sons. Anyway it should be possible to form some kind
Jagiellonian Empire.