We propose a scheme of multilayer thermoelectric engine where one electric current is coupled to two temperature gradients in three-terminal geometry. This is realized by resonant tunneling through quantum dots embedded in two thermal and electrical resisting polymer matrix layers between highly conducting semiconductor layers. There are two thermoelectric effects, one of which is pertaining to inelastic transport processes (if energies of quantum dots in the two layers are different), while the other exists also for elastic transport processes. These two correspond to the transverse and longitudinal thermoelectric effects, respectively, and are associated with different temperature gradients. We show that cooperation between the two thermoelectric effects leads to markedly improved figure of merit and power factor, which is confirmed by numerical calculation using material parameters. Such enhancement is robust against phonon heat conduction and energy level broadening. Therefore, we demonstrated cooperative effect as an additional way to effectively improve performance of thermoelectrics in three-terminal geometry.

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