Is it permissible to combine (in marriage) the daughters of the Prophet, peace and blessings be upon him, with marriage to other women?

Marrying one of the Prophet's daughters and another woman under the same man is permissible in principle. However, if this leads to harming the Prophet, peace and blessings be upon him, then it is not permissible. This is indicated by the Hadith of Ali, may Allah be pleased with him, when he intended to marry the daughter of Abu Jahl. This was due to two reasons: first, that it would harm Fatimah, thereby harming the Prophet, and second, the fear of discord for her due to jealousy.