"An indication of their special relationship is found in the fact that Ali never married another woman as long as Fatima was alive. Sunni sources explain this curiosity in a tradition in which Ali asks for Abu Jahl's daughter in marriage, but the Prophet does not allow him to marry her because it would upset Fatimah."
Denise L. Soufi, "The Image of Fatima in Classical Muslim Thought," PhD dissertation, Princeton, 1997, p. 51-52
I cannot understand why Prophet Mohammed did not let Ali to marry another woman while Islam gives permission to a man to marry four wives? If Fatimah can be upset so every woman whose husbands marry more than one wife can be upset, right? When God allows men to have four marriage, why Prophet Mohammed said no?