Bekiaris et al. (1993, 1996) presented a thorough study of the existence of multiple steady states in homogeneous and heterogeneous ternary azeotropic distillation based on the analysis of the case of infinite reflux and an infinite number of trays (infinity/infinity case). In this paper, first we show how the infinity/infinity analysis and predictions can be extended to quaternary mixtures. Next,the implications of these multiplicities for column design, synthesis, and simulation are demonstrated. More specifically, we show how the infinity/infinity predictions can be useful for the selection of the entrainer, the equipment, and the separation scheme. We show that, in some cases,the column operation at an unstable steady state may have some advantages. The important issue of the effect of the thermodynamic phase equilibrium on the existence of multiplicities is discussed. Using the infinity/infinity analysis, we identify entire mixture classes for which multiplicities are inherent and robust. Mixtures with ambiguous VLE data are studied; we show that in some eases a slight VLE difference between models and/or experimental data may affect the existence of multiplicities while other, major VLE discrepancies do not. Finally, we identify the key issues and the pitfalls one should be cautious about when designing or computing the composition profile of an azeotropic distillation column with a commercial simulator.