We investigate the interactions between exciton-polaritons in N two-dimensional semiconductor layers embedded in a planar microcavity. In the limit of low-energy and low-momentum 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, with the latter vanishing in the zero-momentum limit. We furthermore show that the polariton interactions have a highly non-trivial dependence 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 medal dichalcogenides. This has consequences for the pursuit of polariton condensation and other interaction-driven phenomena in these materials.