In thermoelectrics, band engineering has long been an important strategy for optimizing electronic transport. However, conventional chemical approaches such as doping and alloying alter the composition and typically introduce additional point-defect scattering of charge carriers, limiting the achievable performance. Here, we demonstrate a pressure-driven route that combines multiple band engineering effects without intentional chemical doping or alloying, taking the quasi-one-dimensional (quasi-1D) chain-like semiconductors BiXI (X = S, Se) as a model system. The strong structural anisotropy endows conduction-band valleys at different k points with distinct pressure responses. First-principles calculations show that pressure merges the two lowest conduction-band valleys in momentum space while converging two higher valleys in energy, and this four-band alignment simultaneously enhances the carrier mobility and the density-of-states effective mass. In-situ high-pressure transport and Hall-effect measurements confirm the resulting synergistic optimization: the Seebeck coefficient is largely retained while the electrical conductivity increases sharply, raising the average power factor by a factor of approximately 5-8 between 1 and 6 GPa. This study establishes physical pressure as a clean band-engineering tool and points toward strain-based routes for realizing similar multiband alignment at ambient pressure.