A number of metal systems exhibit positive heat of mixing between the constituent elements and consequently they are immiscible and cannot form alloys. Some classical examples of these systems are Ti–Mg, Zr–Nb, W–Cu, Ni–Ag, and Cu–Fe. We have investigated the alloying behavior of the Ni–Ag, Ti–Mg, and Zr–Nb systems through two solid-state non-equilibrium processing techniques, viz., mechanical alloying and high-pressure torsion. Increases in solid solubility limits have been achieved in all the systems, although the magnitude of the increase is different in the different alloy systems. The results obtained are also different depending on the technique employed and the lattice strain introduced into the system. The extent of increase in solid solubility limits has been rationalized in terms of the heat of mixing between the constituent metals and it is shown that the solid solubility limit is higher the smaller the positive heat of mixing.