The response of the ocean's meridional overturning circulation (MOC) to increased greenhouse gas forcing is examined using a coupled model of intermediate complexity, including a dynamic 3D ocean subcomponent. Parameters are the increase in CO2 forcing (with stabilization after a specified time interval) and the model's climate sensitivity. In this model, the cessation of deep sinking in the north "Atlantic" (hereinafter, a "collapse"), as indicated by changes in the MOC, behaves like a simple bifurcation. The final surface air temperature (SAT) change, which is closely predicted by the product of the radiative forcing and the climate sensitivity, determines whether a collapse occurs. The initial transient response in SAT is largely a function of the forcing increase, with higher sensitivity runs exhibiting delayed behavior; accordingly, high CO2-low sensitivity scenarios can be assessed as a recovering or collapsing circulation shortly after stabilization, whereas low CO2-high sensitivity scenarios require several hundred additional years to make such a determination. We also systemically examine how the rate of forcing, for a given CO2 stabilization, affects the ocean response. In contrast with previous studies based on results using simpler ocean models, we find that except for a narrow range of marginally stable to marginally unstable scenarios, the forcing rate has little impact on whether the run collapses or recovers. In this narrow range, however, forcing increases on a time scale of slow ocean advective processes results in weaker declines in overturning strength and can permit a run to recover that would otherwise collapse.