In this article, we take the tetrahydrofuran (THF)/ethanol (ETOH)/methanol (MeOH) as an example to investigate the process design of the triple-column pressure-swing distillation (TCPSD) for the separation of Serafimov’s class 2.0-2b mixtures with different feed composition. Two basic topology structures (TSI, TSII) and two separation sequences (SSI, SSII) are investigated, then, process optimization with total annual cost (TAC) as objective function is conducted via genetic algorithms. Heat integration (HI) is also applied to TCPSD. From a new perspective, the separation of THF/ETOH/MeOH can be regarded as the azeotropic distillation for THF/ETOH with MeOH as azeotropic agents based on thermodynamic features of Serafimov’s class 2.0-2b mixtures. The feasible topology structure and separation sequence of TCPSD for Serafimov’s class 2.0-2b mixtures depend on the feed composition and operating pressure. The feed composition is divided into three regions according to the concentration of methanol in azeotropic distillation column. The two critical points are azeotropic points at allowed minimum and maximum operating pressure. Especially, when feed composition is below azeotropic point at allowed minimum operating pressure, TSI is not feasible due to less MeOH as azeotropic agents. Furthermore, TCPSD combining pure azeotropic agents (ATPSD) can be developed based on this new insight. Then, two feed compositions are used to illustrate the detailed conceptual design of three topology structures as well as corresponding two separation sequences and their economic performance. The results show that when feed composition is 0.4ETOH/0.25THF/0.35MeOH, TSI and TSII are feasible, the best economical configurations without and with heat integration is TSII-SSII and TSII-SSII-HI. When feed composition is 0.4ETOH/0.4THF/0.2MeOH, TSII and ATPSD are feasible, the best economical configurations without and with heat integration is ATPSD-SSI and ATPSD-SSI-HI. Furthermore, ATPSD-SSI and ATPSD-SSI-HI have 18.28% and 19.38% TAC reduction than TSII-SSI and TSII-SSI-HI, respectively. In summary, feasible and the best economic topology structure and separation sequence of TCPSD for Serafimov’s class 2.0-2b mixtures depend on the feed composition and operating pressure. In addition, the proposed ATPSD shows good economic performance for Serafimov’s class 2.0-2b mixtures.