This study examines a simple 6-box model of a single pole-to-pole ocean basin. Each of a northern "polar gyre," a southern "polar gyre," and an "equatorial gyre," consisting of north and south subtropical gyres plus the equatorial region, is represented by two boxes: a surface box receiving constant fluxes of both temperature (heat) and salt (freshwater) and a deep box. The model includes four dominant processes: surface flux forcing, horizontal meridional advection driven by Southern Ocean winds, horizontal eddy diffusion at gyre boundaries, and convection, as well as the process of vertical diffusion by small-scale processes. Provided that heat loss from the northern polar gyre is sufficiently larger than that from the southern polar gyre, a steady-state Atlantic Meridional Overturning Circulation (AMOC)-like system, i. e., one with sinking in the north polar gyre and upwelling in a weakly stratified southern polar gyre, is obtained at present values of RF ≡ βFS / αFT, the ratio of surface forcing by fluxes of temperature (T ) and salinity (S ) in the equatorial gyre. Despite the fact that vertical diffusive fluxes are much smaller than those associated with all the other processes, it is shown that implementation in this model of a simple water mass–based representation of different vertical diffusivities for T and S, the two water properties that, with pressure, determine the density of seawater, can lead to profound change in the steady-state modes of the system. With equal diffusivities, the AMOC-like mode with north polar convection shifts abruptly to a mode with equatorial convection at sufficiently large values of RF. With unequal diffusivities, this mode boundary is replaced by an intermediate region of RF values in which all three gyres are stratified. The existence and extent of this stratified regime is shown to result predominantly from the differences between vertical turbulent diffusivities of T and S in the "salt fingering" equatorial gyre. Existence of a stratified regime at values of RF somewhat larger that present implies a tendency towards stable stratification throughout the oceans if, under climate change, the equatorial diffusivity difference were to increase as a result of water mass changes in the subtropical gyres and/or an increase in RF as a result of increased atmospheric freshwater fluxes and/or decreased heat fluxes. This tendency towards an everywhere-stratified ocean is independent of that expected from increased freshwater addition to surface polar oceans due to ice melt.