An algorithmic approach is presented for synthesising novel sequences for separating, by distillation and decanting, ternary heterogeneous azeotropic mixtures. Existing synthesis procedures that consider only simple single-feed columns with decanters and integrated decanters are extended to include more industrially relevant options such as columns with several heterogeneous stages, double-feed columns, columns with intermediate decanters, and those accepting a heterogeneous liquid feed. With these advanced column configurations included in the synthesis method, a wider range of sequences may be considered systematically, allowing sequences that are more economically attractive than conventional designs to be identified. A case study illustrates the approach.