What were the chances of the Crusades facilitating the Byzantine reconquest of Anatolia, and as a result having a territory and power base akin to Basil in 1025? I assume it would be a pretty long process, perhaps Barbarossa makes it to the holy land and/or the 4th Crusade goes to Egypt, and the Byzantines make gains as a result.
BTW, I don't expect the Empire to be puppet masters, pulling the Crusader strings for its own gain, just exploiting opportunities that Crusader campaigns provided, like IOTL.