In this paper, we investigate the use of reconfigurable intelligent surfaces (RIS) to allow multiple user pairs to communicate simultaneously over the same channel. We propose a Riemannian manifold optimization approach to solve the problem of configuring the RIS passive reflection coefficients to minimize the total interference under constant modulus constraints. We compare the proposed approach to the widely-used semidefinite relaxation approach (SDR) for dealing with the constant modulus constraints. We investigate, using extensive numerical simulations, the effects of various system parameters, such as the number of users, the number of RIS elements, and the fraction of power received through the RIS. Our results demonstrate that RISs can substantially minimize interference allowing multiple user pairs to simultaneously communicate over the same channel and that the proposed approach vastly outperforms the semidefinite relaxation-based approach, which fails to find satisfactory solutions.