The main goal of this work is to determine the melting temperature range and phase composition of multicomponent Ni-based alloys by applying the methods of design of alloys (CALPNAD method) in combination with statistical processing of the results. In particular, the liquidus and solidus temperatures for a number of experimental alloys of the Ni–Cr–Co–Al–(Me) system are calculated. The degree of influence of adhesive-active elements (Ti, Nb, Zr) on the liquidus temperature and phase composition of alloys of this system is established. The approximate content of alloying elements to ensure the required melting point of experimental filler metals is determined. As shown, alloying zirconium significantly reduces the solidus temperature thus significantly expanding the melting range of experimental alloys. This effect is associated with the formation of low-temperature zirconium eutectic. The influence of titanium and niobium on the amount and thermal stability of the $\gamma$'-phase in experimental alloys is studied. The influence of refractory components (Mo, W, Re) on the presence of topologically close-packed (TCP) phases is studied. As noted, partial replacement of tungsten by rhenium in experimental Ni–Cr–Co–Al–(Me)-based alloys significantly reduces the amount of harmful $\mu$- and p-phases.