First-principles calculations revealing insulator-to-metal transitions in Bi₂Te₃ and Bi₂Te₂Se, at 9 GPa and 12.5 GPa, respectively, match with prior experiments. Our electronic band structure calculations and accompanying Boltzmann transport calculations of thermoelectric properties for Bi_2−xSb_xTe_2−ySe_y alloys explain and predict large power factor changes induced by pressure. Complex band degeneracy changes preceding insulator-to-metal transitions significantly alter the density of states near the Fermi level, and foster the disentangling of the unfavorable coupling between Seebeck coefficient and electrical conductivity. Our findings on pressure-induced changes in thermoelectric power factor provide insights for designing V₂VI₃-based high-performance thermoelectric materials through strategies such as alloying, high-pressure processing, and strain engineering.