Hmmm this doesnt make too much sense. The Ottoman sultans claimed the title of Caliph since Murad I conquest of Edirne in 1362. Who will be Caliph? And will the other accept his authority? I think there can only be one Ottoman Caliph.
This is kind of a big deal as the Gazis are important in this period of expansion. Theologically, divine law without a Caliph is not valid, at least in theory. It is his role to act as the bridge between God's will and the community.
This kind of makes it inevitable that, at the very least, there will be one senior and one junior ruler, likely with a strong pressure to unify once more as the politics of it don't really make for two rulers long term.
Or put in Byzantine terms: the Empire of Nicaea and the Despotate of Epirus were both Byzantine states, yet they couldn't abide each other's existence.