The glass-forming ability (GFA) of Fe-Ni-TM alloys, where TM = V, Nb, Cr, Mo, was determined utilizing thermodynamic modeling. Enthalpies of formation of amorphous state were calculated and analyzed along with normalized mismatch entropy and glass-forming ability parameter. All thermodynamic quantities were qualitatively compared with enthalpies of formation of solid solution and experimental results. Due to the fact that FeNi-based amorphous ribbons are used nowadays in magnetoelastic sensors (MES), which can be used in biomedical or chemical applications, discussion is concentrated mainly on the substitution effect of group V and VI transition metals on the improvement of GFA. In this sense, group V elements are preferred, with Nb as the most promising candidate among all analyzed TM elements. This is a consequence of significant differences of potential and density of electrons at the boundary of Wigner-Seitz cell comparing to Fe and Ni, which in turn leads to more negative values of interfacial enthalpy and higher driving force for vitrification.