We report tunable excitation-induced dipole-dipole interactions between silicon-vacancy color centers in diamond at cryogenic temperatures. These interactions couple centers into collective states, and excitation-induced shifts tag the excitation level of these collective states against the background of excited single centers. By characterizing the phase and amplitude of the spectrally resolved interaction-induced signal, we observe oscillations in the interaction strength and population state of the collective states as a function of excitation pulse area. Our results demonstrate that excitation-induced dipole-dipole interactions between color centers provide a route to manipulating collective intercenter states in the context of a congested, inhomogeneous ensemble.