This question already has an answer here:
On the premise that one who accepts the Torah as Moses delivered it to us from Mount Sinai, and considering that Islam considers the Tanach as a holy book, can one accept Muhammad as a prophet and remain Jewish?
In addition to the Torah, we include works after Moses such as Neviim and Ktuvim in the Tanach. Why might someone / some sect not accept the Quran as well? Even during and after the time of the rise of Islam did the Jews add to the store of holy books, ie Gamara and Talmud.
I understand that the Jews originally rejected Muhammad as a prophet due to his campaign for political control. However that seems to be a technical rejection, not a philosophical rejection.