Is it permissible to hold two Friday prayers—sermon and prayer—in one building that houses an Islamic school and a mosque, or two separate sermons—one for the students at the school and the other in the mosque—followed by one prayer in the mosque, keeping in mind that Friday is a school day in America?

It is not permissible to hold multiple Friday prayers in one town according to the majority of scholars, except out of necessity, such as the mosque being too small, because the Prophet (peace be upon him) and his successors did not hold more than one Friday prayer. If that is prohibited in a town, then prohibiting it within a single building is even more appropriate. Therefore, it is not permissible to hold two Friday sermons in the same building, especially if only one prayer will be performed and the students can attend it. Holding multiple Friday prayers in the same mosque without necessity is a reprehensible expansion that is not sanctioned by Islamic law.