Recently it has been suggested theoretically and discovered experimentally that pressure can induce body-centered cubic vanadium to transition to a rhombohedral phase. Here we show using density functional theory calculations that alloying can affect the same transition, and in particular alloying can increase the stability of the rhombohedral phase, reducing the pressure needed to induce the transition. These calculations are full supercell calculations, as opposed to the virtual crystal approximation and other approximate schemes that neglect atomic relaxation and local bonding effects. These results suggest a way in which alloying provides a means of designing this class of exotic phases to be more robust.