How Would A Crusader-Mongol Alliance Work?

[Basileus_Komnenos]

During my studies of the Crusades one thing that I kept seeing in my textbook was the attempts made between various Christian states to try and ally with the Mongols against the various Islamic powers in the Middle East and the Caucausus.

Supposing that the Crusader states had managed to successfully ally with the Mongol Empire or even the Ilkhanate, what would the realistic results of such an alliance bring? How much would the Crusader States have been able to reclaim? How much longer would they have lasted?

How would this alliance affect other subsequent Crusades? Would it be possible for there to be a Christian Mongol Khanate at all as result of greater contact with other Christian powers?

 

[Tessitore]

My first thought is that it'd probably be one of those alliances that are mostly a case of two groups both being hostile to a third and working together to kick the crap out of them. Going by how other such arrangements have gone in history, there's a high likelihood that it would have come to an end once they were done beating up the Muslims.