Is it permissible to build lavatories and a gymnasium above a mosque if there is a need for that, and what are the limits of what is permissible and what is forbidden in this matter?

If a mosque is built independently, its roof and whatever is above it are considered part of it. Building on top of it is not permissible unless it serves a mosque-related interest, such as expanding it for prayer. Restrooms or a sports hall should not be built above the mosque. Rather, restrooms should be built below it, and a sports hall can be built beside the prayer hall or below it, provided there is trustworthy oversight to ensure no Shariah violations or disturbance to the worshippers. This is out of reverence and honor for the mosque, as it is a place of worship and not for other facilities.