The performance of thermoelectric generators (TEGs) can be improved either by the adoption of multi-stage or tapered leg configuration. So far, a hybrid device that simultaneously uses both multi-staging and tapered leg geometry to improve its performance has not been conceived. Thus, we present a thermodynamic modeling and optimization of a two-stage thermoelectric generator (TTEG) with tapered leg geometries using ansys 2020 r2 software. The optimized parameters include the leg height, area, concentrated solar radiation, and external load resistance. First, the X-leg TEG only improves the performance of the trapezoidal leg TEG below a leg height of 3 mm. Beyond 3 mm, the performance of both TEGs become very similar. Long thermoelectric legs provide higher efficiencies, while short legs generate maximum power densities. To obtain maximum efficiencies, the initial leg height of the thermoelectric legs, 1.62 mm, is increased by 517.28%, while the initial leg area, 1.96 mm2, is decreased by 64.29%. Also, the proposed TTEG with tapered legs (trapezoidal and X-legs) improves the exergetic efficiency of the base case, single-stage rectangular leg TEG, by 16.7%. Furthermore, the use of tapered leg TEGs, in single and multi-stage arrangements, reduces the exergy conversion index of conventional rectangular leg TEGs by 1.89% and 0.98%, respectively. Finally, the use of tapered legs and multi-stage configurations increases the thermodynamic irreversibilities of conventional rectangular leg TEGs, thus reducing their thermodynamic stability.