Title says it all; 3 what if's in the Roman (Byzantine) world...
1. What if the rebellion of George Maniakes had succeeded? Konstantinos IX is deposed and the military faction triumphs 39 years early.
2. What if Manuel I never had a son and was succeeded by Bela/Alexios? Potential union with Hungary.
3. What if Alexios III had suddenly developed a backbone and attacked the approaching army of the Fourth Crusade, instead of retreating? A decisive military victory for a vulnerable Emperor.