The design, optimization, and control of thermally coupled distillation sequences with side columns have been extensively studied in the literature. Energy savings of up to 30% have been reported for such systems; further, dynamic simulations show that the theoretical control properties and closed-loop dynamic responses of thermally coupled distillation sequences are better than those of the conventional distillation sequences. In this paper, we have extended the optimization search for the energy required on the separation of a ternary mixture, detecting two feasible solutions for the energy required in the reboiler for the same value of the interconnecting stream (multiple steady states), filling the gap about this topic on these systems. The multiple steady states detected in the thermally coupled distillation sequences (TCDS) were subjected to a controllability analysis and a closed-loop dynamic study. According to the controllability analysis, the steady state with higher demand of energy in the reboiler presented better theoretical control properties than those of the steady state with lower energy requirement in the reboiler. Consistent with the controllability results, when the two steady states were studied under closed-loop using PI controllers, the best dynamic responses for set point tracking and load rejection were exhibited by the steady state design with the higher energy requirement in the reboiler.