The Richtmyer-Meshkov instability (RMI) is investigated in a dilute gas-particle mixture using three-dimensional numerical simulations. This work extends an earlier two-dimensional study [S. Ukai, K. Balakrishnan, and S. Menon, “On Richtmyer-Meshkov instability in dilute gas-particle mixtures,” Phys. Fluids 22, 104103 (2010)] to a larger parameter space consisting of variations in the mass loading and the particle size as well as considering both single-mode and multi-mode interface initializations. In addition, the effect of the presence of particles on re-shock RMI is also investigated. Single-phase numerical predictions of the mixing layer growth-rate are shown to compare well to both experimental and theoretical results. In a dilute gas-particle mixture, the initial growth-rate of RMI shows similar trends compared to previous work; however, the current numerical predictions show that there is an observable increase, not previously predicted, in the growth of the mixing layer at higher mass loadings. For the range of cases considered, an increase as much as 56% is observed. This increase is attributed to additional vorticity production in the mixing layer resulting from inter-phase momentum coupling. Moreover, the presence of particles introduces a continuous drag on the gas-phase resulting in a delay in the time at which re-shock occurs. This delay, which is observed to be as much as 6%, is largest for higher initial mass loadings and smaller particle radii and has a corresponding effect on both the growth-rate of the mixing-layer after re-shock and the final width of the mixing layer. A new semi-analytical correlation is developed and verified against the numerical data to predict the re-shocked RMI growth-rate in dilute gas-particle flows. The correlation shows that the re-shock RMI growth-rate is linearly proportional to the velocity jump at re-shock, the molecular mixing fraction, and the multi-phase Atwood number. Depending on the initial mass loading and particle radii, the re-shock RMI growth-rates were observed to be reduced by as much as 48% in some cases with variations of around 26% in the width of the mixing layer after re-shock.