Deep open-ocean convection is a complex multiscale nonlinear dynamical phenomenon observed in few localized regions of the World Ocean. The results of Whitehead’s ‘tank model’ [Whitehead, Stratified convection with multiple states, Ocean Modelling, 2(3–4), 109–121, 2000] show that the dynamic system, that includes a deep convection in a localized convective site and water exchange with a neighboring ocean basin, can exist in multiple steady states. We generalize this ‘tank model’ for the case of non-zero salinity of the upper layer, which brings the model closer to the real ocean conditions. We then derive exact analytical solutions of the nonlinear transitional dynamics for different model dynamic regimes, and discuss oceanographic implications of the modified model.