In this work, we study the influence of the excitation conditions on power-dependent spin switching and spin multistability of exciton polaritons in planar semiconductor microcavities. We obtain experimental evidence for the influence of a reservoir of nonradiative states which make a determining contribution to the dynamics of polaritons. While the spinor Gross-Pitaevskii equation (SGPE) fails in reproducing some critical experimental trends, an extended set of equations including a nonradiative reservoir allows us to reproduce the experiments quantitatively. We find that the energy renormalization of the exciton field due to the reservoir is crucial to describe power-dependent spin switching. The reservoir is also responsible for the effective repulsive interactions between polaritons of opposite spin obtained in the framework of the SGPE. Two important parameters, the coupling of the spinor polariton fields to the reservoir and the decay of the reservoir, are determined experimentally. We present indications that the reservoir originates from the formation of biexcitons and is constituted of localized exciton states. DOI: 10.1103/PhysRevB.87.045303