In single crystals of the dimer compound Cs3Y2Br9:10% Yb3+ below 31 K, both visible (VIS) and near-infrared (NIR) luminescence intensities were found to exhibit hysteresis as a function of incident NIR intensity and temperature. The optical bistability is intrinsic to Cs3Y2Br9:10% Yb3+ and not a result of an external feedback. Lowering the temperature to 11 K strongly enhances the all-optical switching behavior. The switching on VIS cooperative upconversion and NIR luminescence transitions occurs simultaneously and with opposite polarity reflecting the competition of both emission processes. On/Off switching ratios of up to 4.8 and 1.7 were observed for VIS and NIR luminescence intensities, Using NIR luminescence spectroscopy, differences in the internal sample temperature of up to 7 K were found between the upper and lower branches of the hystereses. A two-level density-matrix model is developed which includes ground- and excited-state interactions and shows that the intrinsic bistability due to a local field different from the external field is strongly amplified by the nonlinear cooperative upconversion process. Alternatively, a rate-equation model is presented which takes the multilevel nature of the ions into account but is more phenomenological in nature. Formally, the two models are shown to be equivalent, and they qualitatively explain all major experimental observations. It is found both theoretically and experimentally that increasing the coupling within Yb3+ dimers and/or decreasing energy migration through the Yb3+ lattice enhances switching and renders it easier to observe intrinsic optical bistability.