The prototype equiatomic high-entropy alloy (HEA) CoCrFeMnNi usually crystallizes into a single solid solution phase with a face-centered cubic (FCC) crystal structure. Under high pressure, the CoCrFeMnNi was reported to have an FCC to HCP polymorphic phase transition. Meanwhile, a similar phase transition was also observed in the CoCrFeNi alloy. Whether the polymorphism is general in HEAs and how does the composition affect the transition remain unclear. To address these questions, we employ in situ high-pressure and high-temperature synchrotron radiation X-ray diffraction, X-ray emission spectroscopy and ex-situ transmission electron microscopy techniques, and systematically investigate the structure evolution of the subgroup medium-entropy alloys of the CoCrFeMnNi HEA under high pressure (e.g., FeCoNiCr, FeCoNiMn, NiCoCrMn, FeCoNi, FeNiMn, FeNiCr, NiCoCr, NiCoMn). The mechanism for the polymorphic FCC to HCP transition is discussed based on the highly composition-dependent phenomena.