We investigate the interactions between exciton-polaritons in N two-dimensional semiconductor layers embedded in a planar microcavity. In the limit of low-energy scattering, where we can ignore the composite nature of the excitons, we obtain exact analytical expressions for the spin-triplet and spin-singlet interaction strengths, which go beyond the Born approximation employed in previous calculations. Crucially, we find that the strong light-matter coupling enhances the strength of polariton-polariton interactions compared to that of the exciton-exciton interactions, due to the Rabi coupling and the small photon-exciton mass ratio. We furthermore obtain the dependence of the polariton interactions on the number of layers N, and we highlight the important role played by the optically dark states that exist in multiple layers. In particular, we predict that the singlet interaction strength is stronger than the triplet one for a wide range of parameters in most of the currently used transition metal dichalcogenides. This has consequences for the pursuit of polariton condensation and other interaction-driven phenomena in these materials.
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