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We demonstrate the occurrence of spatial multistability using laterally confined microcavity exciton-polaritons. By coherently exciting with a blue detuned laser a series of confined polariton modes, we investigate the effects of multistability on the transmitted laser beam as a function of the excitation power. At each threshold of the hysteresis loop, a switching of the mode profile of the laser beam is associated with a significant energy jump of each of the confined polariton modes in the mesa. A simulation of this behavior is achieved with a multimode generalization of the Gross-Pitaevskii equations in the exciton photon basis. The mechanism behind the spatial multistability is identified as a repulsive cross interaction between polaritons in different modes.