This paper presents the synthesis of heat-integrated thermally coupled distillation systems for multicomponent separations. The synthesized new distillation systems employ the thermal coupling and heat-integration principles simultaneously. As a consequence, they have the potential to significantly reduce both the energy and capital costs to a bigger magnitude than the traditional simple column configurations as well as the systems employing either heat integration or thermal coupling alone. First, a subspace of the possible heat-integrated partially coupled (HIPC) configurations with sharp splits has been identified for a multicomponent distillation. A formula is derived to calculate the number of possible HIPC configurations for any n-component mixture. A simple procedure is given to obtain the practical HIPC configurations for an n-component mixture. Then, the possible thermodynamically equivalent structures of the identified HIPC configurations are presented. The other possible heat-integrated thermally coupled distillation systems involving sloppy splits for an n-component mixture are also discussed. These heat-integrated thermally coupled distillation systems constitute a specific search space to look for the optimal distillation systems for multicomponent separations.