The classical thermal coupling between two distillation columns requires two-way communication whereby both vapor and liquid streams are transferred in opposite directions between one specific location in each of the distillation columns. A general framework is presented whereby this classical two-way thermal coupling is converted to a one-way liquid-only transfer. This conversion is achieved by adding one or more distillation sections and a reboiler and/or a condenser with each added section. The resulting equivalent configurations coproduce some of the component product streams from more than one distillation column and are quite flexible. Finally, the techniques developed for this framework are applied to reduce the heat duty of the well-known conventional distillation column configurations with no thermal coupling.