Yes,I have a solution for you Avitus but you have to think quite ruthlessly and with those days standards(not today's) about all four,but before I tell you,it is going to be quite weird to have four very strong European powers
with common borders,with the same language,backround,traditions etc,not been able to unite by 2012:
1) Trebizond,holding Crimaea,expands in south Ucraine and Georgia-a combination of alliances for the purpose of wars to eliminate opponents,royal marriages that carry lands as dowry,alliance with Nicaea and possibly Georgia and the Mongols to eliminate Turks.Trebizond and Nicaea profit the most,Georgia less.Georgia eventually falls to Nicaea and Trebizond.Nicaea expands west and south and takes all eastern islands in the Aegean.Trebizond takes Constantinople.
2) Nicaea expands west(including Dodecanese and ,south(including Cyprus) and east at the turkish principalities up to Syria;later feels strong enough and forces the Syrian gates.....
3)Epirus holds strongly nowday's Albania,defeats the latins,causes war between the Serbs and the latins wears out both and Michael cuts to pieces the Serbs takes most of their land exterminates or expels the unwanted population,repopulates with Greeks,retains Serbs who are Greek speakers.takes children of exterminated parents,grows them up as greek warriors with a Spartan regime training.Extends to Dalmatia,creates a good fleet and sets eyes on Sicily.Defeats Hungarians sets Danube as his border.
4)What is the fourth part?