An equiatomic CoCrFeNiMn high-entropy alloy was processed by severe plastic deformation followed by post-deformation annealing over a range of temperatures and times leading to a wide range of grain sizes from ~ 0.05 to ~ 70 μm. The results demonstrate there is a sharp evolution in grain size and hardness after annealing above 800 °C due to coarsening facilitated by the dissolution of precipitates together with a high rate of diffusion at high temperatures. Grain growth behavior revealed an incremental low value grain growth exponent with increasing annealing temperature together with a high value activation energy for grain growth of ~ 440 kJ mol−1. A critical grain size of ~ 2 µm is proposed in which deformation-induced twinning is suppressed during plastic deformation. Nevertheless, slip and deformation-induced twinning are deformation mechanisms occurring in samples with grain sizes above this critical value. A model is presented for engineering the grain size by controlling the annealing parameters in the fine grain size range to benefit from the advantages of deformation-induced twining in the CoCrFeNiMn alloy.