High throughput first-principles calculations were employed to unravel the thermodynamic stability of two sets of hierarchical phases, β′′′P and β′′′S, in Mg-RE (rare-earth) alloys. The β′′′P orderings (with compositions greater than xRE=0.125) are predicted to form in the Mg-{La,Ce,Pr,Nd,Pm,Sm} binary alloys, thus explaining experimental observations of RE atoms arranged as hexagonal rings in these alloys. Mg-{Sc,Y,Tb,Dy,Ho,Er,Tm,Lu} alloys are predicted to form β′S (xRE=0.125) precipitates without hexagonal ring arrangements. The calculated misfit strains are used to infer the qualitative shapes of the precipitates and their relative aspect ratios. High aspect-ratio precipitates may be formed using alloying elements that encourage the formation of β′′′P. The predictions in this study can be used to inform alloy design of precipitation strengthened magnesium alloys.