The thermally activated pyramidal-to-basal (PB) transition of (c + a) dislocations, transforming glissile pyramidal dissociated core structures into sessile basal dissociated ones, lies at the origin of low ductility in pure magnesium (Mg). Solute-accelerated cross-slip and double cross-slip of pyramidal (c + a) dislocations have recently been proposed as a mechanism that can circumvent the deleterious effects of the PB transition by enabling rapid dislocation multiplication and isolating PB-transformed sessile segments. Here, the theory for solute-accelerated cross-slip is revisited with an explicit atomistic derivation, is extended to include multiple very dilute solute concentrations, and various aspects of the theory are demonstrated computationally. DFT inputs to the theory for a wide range of new alloying elements are presented. The theory is validated by comparing predicted ductility to literature experiments for a range of alloys. The theory is then applied to predict composition ranges for ductility in rare-earth free ternary and quaternary dilute alloys. The wide range of new alloys predicted to be ductile can serve as a guide to experimental development of new ductile Mg alloys. (C) 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.