Total and minimum reflux bounds serve as limiting case scenarios for determining feasibility in azeotropic distillation columns. Specifically, all reachable feed compositions in a staged rectifying or stripping section have been reported as the union of points enclosed by the distillation and pinch-point curves through a desired product. By eigenvalue considerations of pinch bifurcations and geometric analysis of fundamental region structures, the region of all reachable compositions has seemingly been identified. Additional insights are needed to fully characterize the feasible compositions in a subset of azeotropic mixtures. This article describes how sectional profiles can actually cross pinch-point curves and generate a region of additional feasibility outside the one previously reported. It also demonstrates how a substantially larger region between the distillation line and pinch-point curve after the intersection is only accessible by composition profiles going through the extended region. This extended reachable region is explained by evaluating the conditions for a fixed point in composition space. The effect on sectional profiles is illustrated for both an artificially parametric VLE manifold and a nonideal azeotropic system with more than one simple distillation region. Sectional profiles extended beyond the traditional bounds affect coupled sections in a distillation cascade.