In order to efficiently explore the nearly infinite composition space in multicomponent solid solution alloys for reaching higher mechanical performance, it is important to establish predictive design strategies using computation-aided methods. Here, using ab initio calculations we systematically study the effects of magnetism and chemical composition on the generalized stacking fault energy surface (gamma-surface) of Cr-Co-Ni medium entropy alloys and show that both chemistry and the coupled magnetic state strongly affect the gamma-surface, consequently, the primary deformation modes. The relations among various stable and unstable stacking fault energies are revealed and discussed. The present findings are useful for studying the deformation behaviors of Cr-Co-Ni alloys and facilitate a density functional theory based design of transformation-induced plasticity and twinning-induced plasticity mechanisms in Cr-Co-Ni alloys.