  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.
