Thanks. The idea of this is a much more western-oriented Ottoman Empire, one whom the leaders are more in tune for their Roman and Byzantine past. Instead of the title Padishah or Sultan holding prominence, it would be the honorific title of Kayser-i-Rum or Caesar. I'm sure that Mehmed's fascination to emulate ancient Rome would not die upon his death and would continue on amongst his successors.
After annexing Rome, The Emirate of Granada will be their next target, they are either likely to make them vassals, annex them or at least ally with them, it reminds me of the Seas of the Sultan timeline.