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In the separation industry the extractive heterogeneous-azeotropic distillation (EHAD) is a new and powerful innovation, that is capable of making the separation of highly non-ideal mixtures feasible and economical. In the last years there has been much attention paid to the separation of the minimum boiling homogeneous azeotropes. Although maximum boiling azeotropes are fewer in numbers than the minimum boiling ones but their separation is more complicated but it could be solved with the EHAD, too. Since EHAD is not limited to the separation of minimum boiling azeotropes, the separation of the maximum boiling azeotropes is studied in this work. Our work is motivated by industrial problems because there are such maximum boiling azeotropes in the liquid wastes of the fine chemical industry. The separation of highly non-ideal Water–Acetone–Chloroform–Methanol and Water–Ethyl Acetate–Chloroform–Ethanol quaternary mixtures are investigated and optimized in professional flowsheet simulator environment. Total Annual Costs are also determined. The purity requirement is 99.5 m/m% for Chloroform and the bottom product should be as clear as possible in water so that less liquid organic waste has to be incinerated. It is also an important merit of the EHAD that the chemicals in the distillate can be usually reused supporting sustainability. Different solutions for the separations supplemented with heat integration are examined. On the basis of the computer simulations and the experimental verification it can be concluded, the first time on the literature, that the separation efficiency of EHAD is superior also for the separation of the maximum boiling azeotrope mixtures.