Due to spatial scarcity and uncertainties in sediment data, initial and boundary conditions in deep-time climate simulations are not well constrained. On the other hand, depending on these conditions, feedback mechanisms in the climate system compete and balance differently. This opens up the possibility to obtain multiple steady states in numerical experiments. Here, we use the MIT general circulation model to explore the existence of such alternative steady states around the Permian–Triassic Boundary (PTB). We construct the corresponding bifurcation diagram, taking into account processes on a timescale of thousands of years, in order to identify the stability range of the steady states and tipping points as the atmospheric CO ₂ content is varied. We find three alternative steady states with a difference in global mean surface air temperature of about 10 °C. We also examine how these climatic steady states are modified when feedbacks operating on comparable or longer time scales are included, namely vegetation dynamics and air-sea carbon exchanges. Our findings on multistability provide a useful framework for explaining the climatic variations observed in the Early Triassic geological record, as well as some discrepancies between numerical simulations in the literature and geological data at PTB and its aftermath.