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We explore a material design strategy to optimize the thermoelectric power factor. The approach is based on screening the band structure changes upon a controlled volume change. The methodology is applied to the binary silicides and germanides. We first confirm the effect in antifluorite Mg2Si and Mg2Ge where an increased power factor by alloying with Mg2Sn is experimentally established. Within a high-throughput formalism we identify six previously unreported binaries that exhibit an improvement in their transport properties with volume. Among these, hexagonal MoSi2 and orthorhombic Ca2Si and Ca2Ge have the highest increment in zT with volume. We then perform supercell calculations on special quasirandom structures to investigate the possibility of obtaining thermodynamically stable alloy systems which would produce the necessary volume changes. We find that for Ca2Si and Ca2Ge the solid solutions with the isostructural Ca2Sn readily forms even at low temperatures.