Research on exothermic reactor operation has been based mostly on the classic two-state continuous stirred tank reactor model, implicitly assuming that the cooling jacket temperature dynamics are negligible. In this case, the cooling jacket temperature is the manipulated input instead of the cooling jacket flow rate for feedback control of reactor temperature. Adding a cooling jacket energy balance results in much more complex behavior than a simple lag effect. A stabilizing inner-loop cascade controller is assumed in the two-state CSTR model, because the three-state model incorporating cooling jacket temperature dynamics may be open-loop unstable when the two-state model is open-loop stable. The influence of design parameters on the multiplicity behavior of a three-state model is considered. Elementary catastrophe theory is used to study the effect of process parameters such as the cooling jacket flow rate, heat-transfer coefficient, heat of reaction, and cooling jacket feed temperature on the steady-state multiplicity of the three-state model. This multiplicity analysis is particularly relevant for control because the primary bifurcation parameter is the cooling jacket flow rate, the manipulated input for feedback control in the three-state model. This multiplicity analysis guides improvements in process design and/or operation to eliminate difficult operating regions associated with steady-state multiplicities; the presence of multiple steady states results in safety and operation problems due to ignition/extinction phenomena. Reactor scale-up affects the presence of these infeasible reactor operating regions. Certain design parameter changes that remove multiplicities in the two-state model cannot remove multiplicities in the three-state model.