A 16-box model of the global ocean circulation is constructed to investigate the sensitivity of the thermohaline circulation to upper-ocean density perturbations. The model attempts to represent the main geographical components of the global ocean and is tuned to give a present-day circulation broadly compatible with observed volume fluxes. Extensive tests are made of the model's sensitivity to upper-ocean density perturbations, equivalent to a range of plus or minus 3 psu in salinity about the current climate. It is found that there are seven separate modes of thermohaline circulation that can occur within the model's constraints, as well as the possibility of significant variations in the strength of the current circulation mode. These modes are related to possible changes in surface forcing, such as the abrupt increase in freshwater from ice-sheet melting, where such a possibility exists. A mode with North Atlantic upwelling rather than deep- or bottom-water formation was found to occur with large additional inputs of freshwater to the northern Atlantic. These freshwater inputs needed to be equivalent to an instantaneously reduction of upper-ocean salinity by at least 1.8 psu. The model was unable to produce deep-water formation in the northern Pacific, although this may be a constraint of the model formulation. Bottom-water production was possible in the Indian and Pacific Oceans provided the surface density was much enhanced, beyond likely changes in evaporation and precipitation.