The influence of four-particle correlations on the nonlinear optics of a semiconductor microcavity is determined by a pump-and-probe investigation. Experiments are performed on a nonmonolithic microcavity which contains a ZnSe quantum well. In this system the biexciton binding energy exceeds both the normal-mode splitting between exciton and cavity mode and all damping constants. Oscillatory spectral features below the excitonic resonance are observed in the response for counterpolarized beams. Comparison with model calculations shows that in this case the coherent nonlinearity is dominated by biexciton-exciton interactions beyond the Hartree-Fock approximation.