In order to reconcile Talonschild's, mine, and LoE's suggestions:
The Ottoman Empire is less like the Ottoman Empire of old, and more like a feudal Caliphate or the HRE in Europe. Despite nominally being a nation where the rulers of the various city-states and principalities are vassals of the Emperor in Istanbul, in reality the local rulers have significant autonomy, to the point where one of the claimants to the Caliphate is literally ruling Trebizond and the Sultan in Istanbul can do nothing about it.
However, even this high level of autonomy is not enough. Much of Arabia and the Levant is in full rebellion, egged on by the other Three Caliphs in Persia seeking to overthrow the Sultan and establish one of the Four Caliphs in his place as Caliph of all Islam. In Anatolia, armies loyal to various Caliphs roam and the Sultan roam almost freely, with some of the rebel armies led in absentia by the Caliphs in Persia.
Frequently, cities simply roll over and accept the rule of whatever army is nearby, and in practice the citystates are mere military dictatorships paying lipservice to various Caliphs and the Sultan, with the exception of Trebizond and the cities under its rule which is a theocracy led by the Caliph of Trebizond, Piri Reis.
Meanwhile, the other powers watch and cackle as the Ottoman Empire consumes itself. The Persians host the Three Caliphs and supply their armies in Arabia and Anatolia with weapons and technology, with Persian sky-dhows frequently docking in Trebizond to deploy more equipment. Meanwhile, the Merchant dynasties of southern Europe also plot to bring about the destruction of the Ottomans, supporting the factions in the cities of the Levant - the de Medicis, currently ruling Florence, Bologna and Abruzzi, have made great inroads into Jaffa, the Ferrarias (currently ruling Venice) have taken control of Antioch after a brutal coup in which they murdered the supporters of the previous dynasty there, and the newly rising Vukovics of Belgrade have recently captured Haifa.