From a design perspective, nothing is exceptional about equiatomic high-entropy alloys (HEA), save maximal entropy. Rather, using alloy design concepts non-equiatomic HEA offer a huge design space to tune for optimal properties, with only slightly reduced entropy. We apply high-throughput KKR-CPA to predict stability of N-component HEA in A1, A2, A3, and A4 phases, where the coherent potential approximation (CPA) handles chemical disorder during charge self-consistency. We also address short-range order dictated by N(N–1)/2 pair correlations to guide alloy design. We exemplify predictions in Ti-Zr-Ta-Mo-W to narrow the 5D design search space, and we perform experimental validations. Supported by the U.S. DOE, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division for theory development, and by the Office of Fossil Energy, Cross-cutting Research program, for code validation for HEAs, and experimental validation. Ames Laboratory is operated for DOE by ISU under Contract DE-AC02- 07CH11358.