To enhance the hardness of tungsten tetraboride (WB4), a notable lower cost member of the late transition-metal borides, we have synthesized and characterized solid solutions of this material with tantalum (Ta), manganese (Mn), and chromium (Cr). Various concentrations of these transition-metal elements, ranging from 0.0 to 50.0 at. %, on a metals basis, were made. Arc melting was used to synthesize these refractory compounds from the pure elements. Elemental and phase purity of the samples were examined using energy-dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD), and microindentation was utilized to measure the Vickers hardness under applied loads of 0.49-4.9 N. XRD results indicate that the solubility limit is below 10 at. % for Cr and below 20 at. % for Mn, while Ta is soluble in WB4 above 20 at. %. Optimized Vickers hardness values of 52.8 +/- 2.2, 53.7 +/- 1.8, and 53.5 +/- 1.9 GPa were achieved, under an applied load of 0.49 N, when similar to 2.0, 4.0, and 10.0 at. % Ta, Mn, and Cr were added to WB4 on a metals basis, respectively. Motivated by these results, ternary solid solutions of WB4 were produced, keeping the concentration of Ta in WB4 fixed at 2.0 at. % and varying the concentration of Mn or Cr. This led to hardness values of 55.8 +/- 2.3 and 57.3 +/- 1.9 GPa (under a load of 0.49 N) for the combinations W0.94Ta0.02Mn0.04B4 and W0.93Ta0.02Cr0.05B4, respectively. In situ high-pressure XRD measurements collected up to 65 GPa generated a bulk modulus of 335 +/- 3 GPa for the hardest WB4 solid solution, W0.93Ta0.02Cr0.05B4, and showed suppression of a pressure-induced phase transition previously observed in pure WB4.