The motion-induced drag force acting on a particle moving parallel to an arrangement of N objects is analyzed. Particular focus is placed on the nonequilibrium statistics of the interaction and on the interplay between the system’s geometry and the different dissipative processes occurring in realistic setups. We show that the drag force can exhibit a markedly nonadditive enhancement with respect to the corresponding additive approximation. The specific case of a planar cavity—a relevant configuration for many experiments—is calculated, showing an enhancement of about one order of magnitude. This and similar configurations are of significant potential interest for future measurements that aim to detect the drag force.