Pump-probe measurements in a microcavity containing a quantum well show that a population of circularly polarized (sigma(+)) excitons can completely inhibit the transition to sigma(-) one-exciton states by transferring the oscillator strength to the biexcitonic resonance. With increasing pump intensity the linear exciton-polariton doublet evolves into a triplet polariton structure and finally into a shifted biexciton-polariton doublet. A theoretical model of interacting excitons demonstrates that the crossover from exciton to biexciton polaritons is driven by three-exciton Coulomb correlation.