So, peculiar as it sounds, I'm curious as to whether this could be possible.
PoD - Constantine XI, rather than dying/disappearing in 1453 after the siege of Constantinople, instead accepts an earlier offer of surrender, with an addendum that the Roman people are allowed to follow him wherever he goes, with the Ottomans Support and Blessings.
PoD2 - Genoa, after 1453, and the later seizure of Pera, grants him sanctuary, on the pressings of Giovanni Guistiani - Constantine is granted sanctuary on the isle of Corsica - and later rule on the arrival of significant numbers of immigrants from the Roman Empire in the East.
What is the potential future of this (effectively) reborn Roman 'Empire' given sanctuary on the edge of Italy? What could be done with this premise?