Under high strain-rate loading, prominent increases in pressure usually triggers phase transition (PT), but the concomitant temperature rise may also cause melting. Quasi-isentropic (QI) compression provides a strategy to explore solid-state phase transition by reducing the temperature rise while retaining high pressure. Using large-scale molecular dynamics simulations, we investigate PTs in single crystal CoCrNi medium entropy alloys (MEAs) under QI compression. With the applied strain rates ranging from 108 s−1 to 1011 s−1, the strain-rate dependence and anisotropy of yield stress and solid-state PT path are revealed by comparing the mechanical responses along three compressed crystallographic orientations ([100], [11¯0], and [111]). Positive strain-rate sensitiveness is found in the yield stress along the [11¯0] and [111] directions, while insensitiveness along the [100] direction. Various PTs occur alongside massive plastic deformation in the post-yield regime. As the strain rate rises, face-centered-cubic (FCC) to body-centered-cubic (BCC) PT overrides the stacking fault-induced hexagonal-close-packed (HCP) phase formation and dominates the plasticity for the [100] loading. By contrast, crystalline PTs give way to amorphization for [11¯0] and [111] loading at high strain rates. Chemical short-range order hinders dislocation slip and promotes dislocation interactions, which further facilitate early formation of the BCC phase, suggesting a potential strategy to tailor polymorphism in MEAs.