WI Fourth Crusade sacks Constantinople but they do not institute a Latin Empire?

In 12 April 1204 the Crusaders of the 4th Crusade entered the city of Constantinople after a 2-months siege... In OTL after sacking the Imperial city they divided the ruined empire amongst them...
WI Crusaders were happy with the booty from Constantinople and they left for Jerusalem without dividing the lands of the Empire? Could it be possible tohand over the city to a claimant of the Byzantine Crown and leave?
Any thoughts?
 
Constantinople

Not very likely, unless they felt threatened by a Greek army in the area. A city like Constantinople was too large and rich to leave after capturing it. If a crusading army was not in a position to hold it, then I'm the Venetians would have gladly taken up the offer for commercial reasons.
 
Constantinople

The Venetians took Crete, and other Greek territories after the 4th crusade. Eventually they got Cyprus in the 15th century. You know how greedy they were!.
 
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