An experimental and theoretical study of optical multistability in a double resonator system formed by a thin single crystal of GaSe and an air gap separating it from a dielectric mirror is reported. The system allows one to observe various types of optical hysteresis, bi-and multistability with microsecond switching time at room temperature and submilliwatt threshold of first switching. Five stable output states are reported for a given input. A nonmonotonic input/output characteristic of the double resonator system is used to demonstrate doubling of the incident laser modulation frequency as a new example of an all-optical signal processing.