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We have studied the influence of additions of Al and Si on the lattice stability of face-centred-cubic (fcc) versus hexagonal-closed-packed (hcp) Fe-Mn random alloys, considering the influence of magnetism below and above the fcc Neel temperature. Employing two different ab initio approaches with respect to basis sets and treatment of magnetic and chemical disorder, we are able to quantify the predictive power of the ab initio methods. We find that the addition of Al strongly stabilizes the fcc lattice independent of the regarded magnetic states. For Si a much stronger dependence on magnetism is observed. Compared to Al, almost no volume change is observed as Si is added to Fe-Mn, indicating that the electronic contributions are responsible for stabilization/destabilization of the fcc phase.