This paper focuses on multi-user downlink signal transmission in a wireless system aided by multiple reconfigurable intelligent surfaces (RISs). In such a multi-RIS, multi-user, multi-antenna scenario, determining a set of RIS phase shifts to maximize the sum throughput becomes intractable. Hence, we propose a novel scheme that can substantially simplify the optimization of passive beamforming. By opportunistically selecting a user with the best channel condition as the only active transmitter in the system, it degrades to single-user passive beamforming, where two methods, i.e., joint optimization based on the semidefinite relaxation approach and alternating optimization, are applicable. The superiority of the proposed scheme is demonstrated through Monte-Carlo simulations.