In this study, we used atomistic simulation methods to examine solid-solution phase formation rules for CoCrFeNi high entropy alloy. Using the Monte Carlo simulations based on the modified embedded atom method (MEAM) potentials, we sampled the thermodynamically equilibrium structures of the CoCrFeNi alloy and further predicted that the CoCrFeNi alloy could form a solid solution phase with high configurational entropy of 1.329R at 1373 K. Furthermore, we examined the stability of this solid solution phase of the CoCrFeNi alloy against the well-recognized solid-solution phase formation rules by varying the MEAM potentials and thus tuning the atom size and mixing enthalpy in the alloy. Our simulation results revealed that it required atom size difference effect $$ \left| \delta \right| < 0.05 $$ and mixing enthalpy effect −10 kJ/mol < ΔH ≈ 0 kJ/mol for the modeled CoCrFeNi alloy to remain a single solid solution phase.