Is it permissible to build an additional floor in a shared house and invest it for a specified period, after which whoever wishes to share would pay his portion to benefit from it? And would this be considered usury (riba)?

The aforementioned cooperation is not usury (riba); rather, it is permissible as long as there is mutual consent, for the air is shared among the partners. It is permissible for the brothers to lend their share of the air for construction for a known period. If mutual consent for sharing in the construction is not reached after the agreed-upon period, the lenders are given the choice between demolishing the structure or paying the value of the structure as if dismantled.