High-entropy alloys (HEAs), i.e., multicomponent alloys where (typically five or more) elements are combined in equal, or roughly equal, quantities, are of great current interest, due to their formation of single, simple structured phases, and the unusual properties they can potentially exhibit. Phase presence may be predicted using semi-empirical methods, but deviations from predictions may be seen during the course of alloy synthesis, with the formation of unexpected phases. The generation of such phases may be controlled with knowledge of the effective solidification temperature; in this full article, Chvorinov’s rule for solidification time is used to estimate this temperature as part of the design of a new multiphase alloy system, TiVCrZr-Si_x. Further heat treatment of the TiVCrZr-Si system confirms the applicability of this approach. The new compositions demonstrate mechanical properties that suggest potential for optimization for high-temperature applications.