The Aegean world in the year 1415.
The POD for this is sometime in the 1270s, I'm not entirely sure exactly when. Basically, the reconquest of Constantinople goes as planned, and the Roman Empire is briefly reinvigorated. The difference here is that Michael VIII is succeeded by a man of talent and competence, John III, who does all he can to squeeze resources out of the Byzantine state. In doing so, John makes himself extremelly unpopular, but puts the Empire back on a relatively sound economic footing by pursuing a strong alliance with Genoa, and roundly defeating the Ottomans. However, the Empire falls into a vicious civil war around 1310, and suffers a series of defeats to various foes. She survives only thanks to the alliance with Genoa, and her strong navy.
Elsewhere in the Mediterranean, the Crusader kingdom of Cyprus falls to a Mameluke invasion in 1328, forcing around 10,000 displaced knights and the monarchy to flee westward. They eventually form an alliance with George Palaiologos, a pretender to the Byzantine throne, and help him to become Emperor, in exchange for the surrender of Rhodes as a new base for them. The Crusaders then eagerly take the fight to the small, divided Turkish states of Lydia, conquering much of the region by 1350, and establishing their capital at Philadelphia. The new Kingdom of Philadelphia exists as a close ally of the Roman Empire.
Meanwhile, to the East, the remaining Turkish groups on the Anatolian plateau are eventually unified by the Karamanids, operating from a Mediterranean base. The north coast of Anatolia, however, remains independent under the Empire of Trebizond and a couple of small Turkish ghazi states, while in the west, the remnant Ottomans, together with the Goynuk Turks, continue to have their independence bankrolled by Constantinople. The Romans are eager to put up buffer states between the power of Karaman and their prosperous towns and villages around the coast of the Sea of Marmara.
In the Balkans, Serbia and Bulgaria vie for Great Power status, each seeking the support of the Emperor in Constantinople in achieving this. Currently, the Emperor Manuel III supports the Serbs, and provides them with Aegean ports, but the moment Serbia begins to look too threatening, he can confidently be expected to switch his alliance back to the Bulgars. Both Slavic states are evenly matched, leading to constant, grinding warfare between them.
Any further questions and queries welcome!