We show how the limiting operating conditions, total reflux and thermodynamically optimum operation, can be used to determine the feasibility of a desired separation by continous distillation. To assess feasibility, so-called pinch point trajectories are established as the limits of separations achievable in each column section. These trajectories may be determined graphically using residue curve maps. The feasibility criterion is generalized to result in a method to establish the ranges of top and bottom product compositions achievable by a single-feed distillation column for a given ternary feed. One particularly interesting application is to reveal where and to what extent distillation boundaries for azeotropic mixtures, derived for total reflux, can be surpassed in columns operated at finite reflux ratios. We present a criterion to estimate the maximum reflux for such separations and illustrate process schemes that exploit the possibility of crossing of total reflux boundaries to separate azeotrope-forming mixtures. Finally, we demonstrate how intermediate heat exchangers can be used to improve separations of azeotropic mixtures across total reflux boundaries