That could work. Attempt to mold a monotheistic understanding with the Muslims and Jews to better incorporate them into the Empire.
Our Holy Texts are just basically Vol. 1 is for the Jews, Vol. 2 is for the Christians, Vol 3. is for the Muslims, but overall we are all brothers of the book, just different on how new or old the book we subscribed to is.
Well I doubt that they would take this approach. However, it could be a sense where the theological leanings become such that Islam is seen as a more radical variety of Byzantine Arianism. At least from a Latin perspective. While in the Mid East, a certain level of tolerance develops despite agreement of deep disagreement, between Sunni Islam and Byzantine court Arianism.