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High-latitude Northern Hemisphere climate during the last glacial period was characterized by a series of abrupt climate changes, known as Dansgaard-Oeschger events, which were recorded in Greenland ice cores as shifts in the oxygen isotopic composition of the ice. These shifts in inferred Northern Hemisphere high-latitude temperature have been linked to changes in Atlantic meridional overturning strength. The response of ocean overturning circulation to forcing is nonlinear and a hierarchy of models have suggested that it may exist in multiple steady state configurations. Here, we use a time-dependent coarse-resolution isopycnal model with four density classes and two basins, linked by a Southern Ocean to explore overturning states and their stability to changes in external parameters. The model exhibits hysteresis in both the steady state stratification and overturning strength as a function of the magnitude of North Atlantic Deep Water formation. Hysteresis occurs as a result of two nonlinearities in the model-the surface buoyancy distribution in the Southern Ocean and the vertical diffusivity profile in the Atlantic and Indo-Pacific basins. We construct a metric to assess circulation configuration in the model, motivated by observations from the Last Glacial Maximum, which show a different circulation structure from the modern. We find that circulation configuration is primarily determined by North Atlantic Deep Water density. The model results are used to suggest how ocean conditions may have influenced the pattern of Dansgaard-Oeschger events across the last glacial cycle.