The separation of ternary mixtures with homogeneous or heterogeneous multi-azeotropes has received increasing attention. In this work, a systematic design, optimization and control procedure is proposed for extractive distillation of heterogeneous mixtures with four azeotropes. Herein, the ternary system isopropyl alcohol/isopropyl acetate/water is taken as a case study. The suitable entrainer is first obtained through a proposed approach combining the vapor-liquid equilibrium (VLE) curves and infinite dilution activity coefficient ratios. Conceptual design of two alternative separation sequences involving double-column extractive distillation with a pre-concentrator (DEDP) and triple-column extractive distillation (TED) are then investigated based on thermodynamic insights. With the method of sequential iterative optimization and taking total annual cost (TAC) as the objective function, the two processes are optimized. The optimal results indicate that the DEDP process with dimethyl sulfoxide as entrainer can save 6.43% TAC than that of TED. Finally, a new control structure combining reflux flowrate-to-feed (R/F) and adjustable reboiler duty-to-feed (QR/F) with "HiLoSelect" strategy is proposed to better handle three product purities than that of the basic control structure while feed flowrate and composition disturbances are introduced in the studied DEDP process.