An interatomic potential (termed EAM-21) has been developed with the embedded atomic method (EAM) for CrFeMnNi quaternary HEAs. This potential is based on a previously developed potential for CrFeNi ternary alloys. The parameters to develop the potential were determined by fitting to experimental values, density functional theory (DFT) and thermodynamic calculations, to reproduce the main crystal characteristics, namely: the stability of the fcc phase, elastic constants, and stacking fault energy. Its applicability for the study of plastic deformation mechanisms was checked by calculations of behaviour of a ½<110>{111} edge dislocation in equiatomic quaternary CrFeMnNi alloy, as well as its less-complex subsystems (ternaries, binaries, and pure metals). The calculations were performed in the domain of temperatures between 0 and 900 K; smooth and stable glide of an edge dislocation and fcc phase stability in this temperature range was confirmed. This study demonstrates the suitability of the EAM-21 potential for the analysis of plasticity mechanisms and mechanical properties of CrFeMnNi HEAs.