In transition metal dichalcogenides' layers of atomic-scale thickness, the electron-hole Coulomb interaction potential is strongly influenced by the sharp discontinuity of the dielectric function across the layer plane. This feature results in peculiar nonhydrogenic excitonic states in which exciton-mediated optical nonlinearities are predicted to be enhanced compared to their hydrogenic counterparts. To demonstrate this enhancement, we perform optical transmission spectroscopy of a MoSe2 monolayer placed in the strong coupling regime with the mode of an optical microcavity and analyze the results quantitatively with a nonlinear input-output theory. We find an enhancement of both the exciton-exciton interaction and of the excitonic fermionic saturation with respect to realistic values expected in the hydrogenic picture. Such results demonstrate that unconventional excitons in MoSe2 are highly favorable for the implementation of large exciton-mediated optical nonlinearities, potentially working up to room temperature.