Multi-component alloy Fe-Cr-Mn-Ni is a promising new candidate system not only because of its potential application as structural materials beyond conventional austenitic steels but also for fundamental physics role played by Mn element in Fe-Cr-Ni based alloys. In this work, the phase stability of magnetic face-centered cubic (fcc) Fe-Cr-Mn-Ni system in the full composition range has been studied by the means of spin-polarized Density Functional Theory (DFT) and Cluster Expansion (CE) method. new four-component magnetic Ni4 phase, which has not been described previously in the literature, is predicted as the ground state (GS) for the quaternary system. All experimental GS of underlying fcc binary and ternary subsystems have been consistently reproduced in the present CE model among which the anti-ferromagnetic L10 MnNi hasthe lowest formation enthalpy. Nickel is found to be the most influential element from the points of view of fcc stability and the average magnitudes of magnetic moments of all the elements in the alloy. Theoretical magnetic phase diagram of Fe-Cr-Mn-Ni is found to be in good agreement with available experimental results. The average magnitude of magnetic moment is increasing with volume slower in Fe-Cr-Mn-Ni than in Fe-Cr-Ni that supports the addition of Mn to the Fe-Cr-Ni alloys in order to improve the swelling resistance under irradiation. Order-disorder phase transition temperature and chemical Short-Range Order (SRO) as functions of temperature and composition have been systematically investigated with the Monte-Carlo simulations. The increase of nickel composition in the pseudobinary alloys from 0 to 50 at.% leads to the increase of order-disorder transition temperatures, which is in a variance compared to other constituent elements. Detailed analysis of the  SRO shows an important role of L10 MnNi precipitates in the increases of the order-disorder transition temperature in a wide range of quaternary concentrations, including the near-equiatomic region. The contribution of congurational entropy to the free energy of alloys calculated using the matrix formulation of the CE method shows an important effect on the alloy stability mostly in the intermediate temperature range, where the order-disorder transition takes place.