Alexius had asked for Western mercenaries at first. Instead he got successive armies and leaders that he had to extract pacts of fealty from, with the pledge that lost Byzantine territory would be returned to his control. This didn't work too well later on as the Western forces and Byzantine fell into mutual suspicion.

Well, what if Alexius had a greater degree of control/influence over the enterprise? How implausible is it for the Emperor to assume a direct leadership role for the overall expedition from the very outset?

Secondly, what would have happened if Alexius had not turned back with his army when he met the deserters from Antioch? Would the West-East relationship have held? Would Alexius have continued on to assist in the conquest of Syria? Looking ahead, would the result be stronger, more defensible Crusader states?

If he'd pressed ahead, it may have resulted in stronger ties between the Franks and the Greeks, but they mostly already hated them anyway. If he HAD travelled to Antioch, he would have been in a very dangerous position, and could easily have been cut off. Even a threat to his lines of communication would have forced him to leave, and then the Franks would have just gone right back to hating Greeks again. I think the best he could have hoped for would have been to keep going (I believe it was impossible for him to get there in time to help anyway) simply to create a much stronger claim to Antioch than historically, and then quickly retreat to the empire leaving more loyal Franks behind him. Turning back and never showing up allowed the oaths the crusaders swore to be publicly ignored, but even if it wasn't the Franks were hardly likely to abide by it anyway.

He probably couldn't have garrisoned Antioch, anyway, due to the chronic lack of troops that initially led him to triggering the Crusades. While the Crusaders were heading for Jerusalem, his forces were securing western Anatolia and mopping up the remaining minor Turkish emirs until he ran out of troops. Then he created a no man's land between his reconquered territory and the Turks. Antioch was nominally Byzantine at the start of his reign 20 years before and he didn't have the troops to defend it then, either.

Well, if the pitch for the operation had been limited to "go save the Eastern Empire in exchange for cash and land grants" instead of ballooning into the Crusades, some smaller number of the younger sons of the aristocracy, poorer knights, and other military adventurers who made up a significant part of the historical crusades might have elected to become mercenaries in Byzantine service. The arrival of troops equipped and trained to the standard of Western knights, in this case under his command instead of pursuing their own ends, might have allowed Alexius to retake the Anatolian themes and push the Turks back.

There certainly wouldn't be enough men to achieve a monumentally successful operation like the First Crusade, which had carved out one of the wealthiest and most important centers of the Islamic world in one swoop, but they could have stabilized the situation for the Byzantines and, settled on central Anatolian lands recaptured from the Turks, formed the basis for a permanent "Frankish" military establishment under Byzantine control in the heartland of the Empire. Also, with no First Crusade, there would be no disastrous Fourth Crusade, which had effectively ruined the Empire. So in a best case scenario the Empire would be healthier, perhaps to the point of regaining its pre-Mantzikert borders in Asia Minor, and stabilizing them in a more permanent sense with the injection of new manpower.

The more profound effect, however, would probably be on Western Europe, because of the defining nature of the Crusades on medieval Europe.

---

"I am gravely disappointed. Again you have made me unleash my dogs of war."
--The Lord Humungus