Motor-gear transmission systems often display pronounced torsional oscillations, primarily stemming from their inherent nonlinearity. In the case of these multi-degree-of-freedom systems with nonlinear properties, relying solely on a single multi-stable nonlinear energy sink (MNES) for vibration suppression proves inadequate. In response, a distributed suppression scheme utilizing the MNES-cells is proposed to address multi-modal vibrations in motor-gear systems. The placement of the MNES-cells is determined through sensitivity analysis in conjunction with natural modes. The vibration suppression performance of the MNES-cells is assessed, followed by its replacement with single MNES under consistent inertia conditions. Then, the suppression performance of the MNES-cells is compared to that of the single MNES, and the performance of the MNES-cells is analyzed under various excitation intensities and gear clearances. The results demonstrate that the MNES-cells effectively suppress multi-modal vibrations of the system. This viewpoint is further supported by the experimental findings. In comparison to the single MNES, each member of the MNES-cells effectively dissipates the vibration energy of the primary system. Thus, under identical conditions, the suppression performance of the MNES-cells surpasses that of the single MNES. In steady-state responses, the vibration suppression rate of the MNES-cells increases by 15.84% in simulations and 12.62% in experiments compared to the single MNES.