Density functional and Boltzmann transport theories have been used to investigate the effect of constraints generated by substituting tin for silicon atoms or by inserting antimony atoms into Mg2Si on the electronic and thermoelectric properties of this compound. The investigated hypothetical structures are Mg2Si1-x Sn (x) with x equal to 0.125, 0.25, 0.375, 0.625, 0.75, and 0.875, and Mg8Si4Sb, Mg8Si4Sb3, and Mg2SiSb. The transport properties are presented with respect to the energy at three predefined temperatures and with respect to temperature for low and high electron and hole dopings. The effects of Sn-for-Si substitution are very similar to those observed for Mg2Si subjected to uniaxial and biaxial tensile strains. Overall, the power factor decreases as the doping level or tensile strain increases. In contrast, the maximum of the power factor increases with temperature. Irrespective of the temperature and electron or hole doping levels, the electrical conductivity of the Sb-inserted Mg2Si structures is far higher than that of Mg2Si. In the Fermi level energy region, the Seebeck coefficient S of the Sb-inserted Mg2Si structures is lower than that of Mg2Si. For Mg8Si4Sb3 and Mg2SiSb, the opposite is observed in the region where the electron density is very small (about 2 eV below the Fermi level). As a consequence, the power factor follows the same trends as the Seebeck coefficient.