As a new approach to passive sound control in low-frequency domain, the targeted energy transfer (TET) phenomenon has been investigated inside a three-dimensional (3D) acoustic cavity by considering a two degrees-of-freedom (DOF) system with an acoustic mode and a membrane nonlinear energy sink (NES). The beginning of TET phenomenon of the 2DOF system and the desired working zone for the membrane NES have been defined. In order to enhance the robustness and the effective TET range in acoustic cavities, a 3DOF system with two membranes and one acoustic mode is studied in this paper. We consider two different membranes and two almost identical membranes to analyze the TET phenomenon, respectively. The desired working zone which was obtained by the 2DOF system is applied to analyze the 3DOF system. We observe that two membranes can enlarge the desired working zone.