The challenge of growing rare-earth (RE) sesquioxide crystals can be overcome by tailoring their structural stability and melting point via composition engineering. This work contributes to the advancement of the field of crystal growth of high-entropy oxides. A compound with only small REs (Lu,Y,Ho,Yb,Er)₂O₃ maintains a cubic C-type structure upon cooling from the melt, as observed via in-situ high-temperature neutron diffraction on aerodynamically levitated samples. On the other hand, a compound with a mixture of small and large REs (Lu,Y,Ho,Nd,La)₂O₃ crystallizes as a mixture of a primary C-type phase with an unstable secondary phase. Crystals of compositions (Lu,Y,Ho,Nd,La)₂O₃ and (Lu,Y,Gd,Nd,La)₂O₃ were grown by the micro-pulling-down (mPD) method with a single monoclinic B-type phase, while a powder of (Lu,Y,Ho,Yb,Er)₂O₃ did not melt at the maximum operating temperature of an iridium–rhenium crucible. The minimization of the melting point of the two grown crystals is attributed to the mismatch in cation sizes. The electron probe microanalysis reveals that the general element segregation behavior in the crystals depends on the composition.