Reconfigurable surfaces (RS) have recently emerged as an enabler for smart radio environments where they are used to actively tailor/control the radio propagation (e.g., to support users under adverse channel conditions). If multiple RSs are deployed (e.g., coated on various buildings) to support different groups of users, it is critical to jointly optimize the phase-shifts of all RSs to mitigate their interference as well as to leverage the secondary reflections amongst them. Motivated by the above, this paper considers the uplink transmissions of multiple users that are grouped and supported by multiple RSs to communicate with a multi-antenna base station (BS). We first formulate two optimization problems: the weighted sum-rate maximization and the minimum achievable rate (from all users) maximization. Unlike existing works that considered single user or single RS or multiple RSs without inter-RS reflections, the considered problems require one to optimize the phase-shifts of all RSs' elements and all beamformers at the multi-antenna BS. The two problems turn out to be non-convex and thus are difficult to be solved in general. Moreover, the inter-RS reflections give rise to the coupling of the phase-shifts amongst RSs, making the optimization problems even more challenging to solve. To tackle them, we design alternating optimization algorithms that provably converge to locally optimal solutions. Simulation results reveal that by properly managing interference and leveraging the secondary reflections amongst RSs, there is a great benefit of deploying more RSs to support different groups of users and so as to achieve a higher rate per user. This gain is even more significant with a larger number of elements per RS. In contrast, without properly managing the secondary reflections, increasing the number of RSs can adversely impact the network throughput, especially for higher transmit power.<br>