  We study the stability of a multicomponent exciton-polariton fluid under
resonant excitation within the linear response approximation of a generalized
Gross-Pitaevskii equation. We show that, two spatially homogeneous and
independently tunable pumping lasers produce, for the same values of the system
parameters, up to three stable solutions. Three-stability is understood by
noting that the cavity can be either little or highly populated and, in this
second case, the largest part of the population lies in either one of the two
components. Moreover, we show that easily tunable multistable hysteresis loops
can be performed by the system.
