Pure Mg has low ductility due to a transition of < c+a > pyramidal dislocations to a sessile basal-oriented structure. Dilute alloying generally improves ductility. Enhancement of pyramidal cross-slip from the lower-energy pyramidal II plane to the higher-energy pyramidal I plane has been proposed as the mechanism. Here, the theory is applied to ternary and quaternary alloys of Zn, Al, Li, Ca, Mn, Sn, K, Zr, and Sr at dilute concentrations, and a wide range of compositions are predicted to have good ductility. Interestingly, while Zn alone is insufficient for achieving ductility, its inclusion in multicomponent alloys at 0.5 at.% enables ductility at the lowest concentrations of other alloying elements. Further implications of the theory are discussed.