We propose a scheme for controlling the movement of dimers, trimers, and other multimers in optical lattices by modulating the lattice potential. In deep optical lattices the propagation of deeply bound atomic clusters is slowed by the high energy cost of virtual intermediate states. Adapting the well-known method of lattice modulation spectroscopy, the movement of the clusters can be made resonant by utilizing sequences of bound-bound transitions. Using the scheme, the mobility of each specific cluster can be selectively controlled by tuning the modulation frequency. We formulate a simple and intuitive model and confirm the validity of the model by numerical simulations of dimers and trimers in a one-dimensional optical lattice.