As the 4th Crusade started to go off the rails, the populace of Constantinople began to resign themselves to their fate, and figured that Boniface would likely be declared Emperor. That wasn’t so bad, he had strong dynastic ties to the Angeloi, so they could grudgingly accept him. The Venetians, however, couldn’t, for the exact same reason: he’d actually have some sort of power base independent of them, so they vetoed electing him.
How could we get Boniface on the throne, and how might his reign go? I’m thinking some back room deals whereby some of the nobility, seeing the writing on the wall a little quicker (these being the same nobility that all refused the throne because they knew they would be doomed), accept Boniface as Emperor relatively early during the chaos, before the Latins can truly consolidate in the city. With his own forces, and whatever remains of the Byzantine forces and Varangian guard backing him, could he consolidate his own hold on power relative to the other crusaders? If he does, early enough, not only is the capital spared further destruction (though fire had already ravaged it), he could consolidate a better hold on the rest of the empire.