Using a global coupled model of intermediate complexity (2D atmosphere, 3D ocean), the behavior of the thermohaline circulation is explored for various increased CO2 scenarios. A novel feature of the model is our ability to adjust the model's sensitivity to CO2 increases by changing the strength of the cloud feedback. By varying the rate and duration of increases in atmospheric CO2, the model's sensitivity, and the river runoff scheme for perturbations in freshwater forcing, we are able to obtain and analyze a spectrum of behaviors, ranging from little change in the thermohaline circulation to a full shutdown of sinking in the North Atlantic. Although the initial decrease in overturning strength (i.e., over a centennial time scale) is primarily a function of the rate of CO2 increase, whether the North Atlantic sinking ultimately shuts down is governed by the product of the model's prescribed climate sensitivity and the stabilization CO2. However, if the rate of increase (for a given stabilization level) is sufficiently slow (e.g., over several hundred years), a recovery can occur for a model sensitivity/stabilization combination that collapses given a more rapid increase. Over a portion of phase space a weak, meta-stable overturning circulation exists; once the circulation crosses this threshold, a collapse rapidly occurs.