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A computational thermodynamics approach has been employed to design CoCrFeMnNi-based medium- and high- entropy alloys (M/HEAs) with systematically varied compositions (Co((80-X)/2)Cr((80-X)/2)FeXMn10Ni10 with x = 30, 40, and 50 at.%) and phase stability. Since the formation of sigma phase, usually brittle and undesirable, is a common concern, when this class of alloys is subjected to elevated temperatures (600–1000 ◦C), predicting its formation becomes essential. Thus, its formation and the phase equilibria were studied using the CALPHAD method, and two empirical methods, namely, valence electron concentration (VEC) and paired sigma-forming element (PSFE). Isothermal aging treatments at 900–1100 ◦C for 20 h were performed, since CALPHAD and VEC/PSFE predictions diverged. Both prediction methods were compared with experimental characterization by a combination of scanning electron microscopy and high-energy synchrotron X-ray diffraction. The predictions from the VEC/PSFE and CALPHAD calculations (depending on the database used) were shown to be quite accurate.