In an earlier work (Agrawal, R.; Fidkowski, Z. T. Eng. Chem. Res. 1998, 37, 3444) it was shown that for the distillation of a ternary liquid mixture into pure component product streams the modified direct or indirect split configurations can have higher thermodynamic efficiencies than the conventional thermally coupled configurations. In this paper, thermally coupled column configurations are modified by incorporating intermediate temperature reboilers and condensers to accept/reject heat at the temperatures of boiling/condensing binary mixtures. The modified side rectifier or side stripper configurations retain the low vapor flow of the unmodified configurations. They have the same total number of reboilers and condensers as do the direct or indirect split but they provide higher thermodynamic efficiencies than the corresponding direct or indirect split. These new configurations also provide an additional degree of freedom to shift heat (cold) duty between the intermediate temperature reboiler (condenser) and the reboiler at the warmest temperature (condenser at the coldest temperature). Finally, a more complete ternary and quarterary superstructure is suggested that contains these new configurations as well as all earlier known superstructures and configurations.