Assuming a post-Manzikert Byzantine recovery of Asia Minor, any lasting rule would require significant cooperation with a Turkish populace in inner Asia Minor on Constantinople’s part. At best, this means that the Byzantines will have Turkish auxiliaries to call upon against the Mongols, while at worst it creates a potential fifth column of Mongol support behind the Taurus mountains. Either way, though, I find the prospects of the Byzantines being able to decisively check the Mongol advance through conventional land warfare - a strategy only successfully implemented once - rather unlikely. After all, if the Rumelians were unsuccessful against the Mongols without the handicapping elements of a resurgent Bulgarian Empire threatening their western flank, a history of court intrigue weakening their military capacity (something even the Macedonian Emperors faced) and potentially sedition from their eastern provinces, I don’t see the Byzantines doing particularly better.
However, depending on the status of Constantinople - I do believe it would be tennable to attempt a similar strategy to the First and Second Arab Sieges of Constantinople where Asia Minor is ceded but the capital’s defenses maintained - and assuming that the Mongols do not assert long-term domain over Asia Minor, which they did not do OTL, then the Byzantines would be in a better position to recover Asia Minor than the Rumelians were, as their core imperial apparatus would be maintained. That is, of course, assuming that no western powers get involved against a Constantinople that is distracted by the massive Mongol threat to the east, or that the Mongols, who were experts in siege warfare, did not manage to take Constantinople.