Abstract: Nonlinear energy sink (NES) possesses numerous advantages, such as a wide vibration reduction frequency bandwidth and excellent damping performance. However, NES has no linear stiffness, which makes it difficult to drive NES vibrator with large weight, so it is difficult to be applied to reduce the vibration of large engineering structures. Therefore, the efficient and convenient application of NES in engineering vibration mitigation remains a subject of ongoing research. Assembling NES in the form of cells within the vibrating primary structure, allowing multiple NES cells to act collectively, is a promising vibration reduction strategy. The damping effects of multiple NES cells on a vibrating structure, significantly heavier than a single NES, under the excitation of an eccentric rotor are explored in this paper. The overall response characteristics of a system composed of multiple coupled NES cells and the primary structure are analyzed. The governing motion differential equations are established, and the Complexification-Averaging (CxA) method is employed to derive approximate analytical expressions for steady-state response and the slow invariant manifold of the system. Stability analysis of steady-state solutions is conducted through the perturbed motion differential equations of the slow manifold. The pseudo-arc length method is then utilized to obtain approximate solutions for the response of the system. The vibration reduction effect of the NES cells and the characteristics of the response of the system are studied, and verification is performed using the Runge-Kutta (R-K) method. The results demonstrate that by the collective action of multiple NES cells, the vibration of the primary structure with large weight can be controlled effectively. The vibration reduction efficiency increases notably with the number and weight of NES cells. The response state in the resonance region transitions from a stable state to a strongly modulated state, and then back to a stable state as the number of cells increases. Hence, this study contributes to the engineering application of NES.