The behavior of reactive column section profiles under arbitrary reaction distribution policies is addressed through the use of difference points. We develop a method to capture the effects of reaction distribution and show how the placement of reaction within a section controls the path of the profile. We also investigate the relationship between reaction distribution and sectional flow rates and compositions which leads to a set of feasibility criteria that must be maintained as profiles proceed from stage-to-stage. Finally, the termination conditions for reactive profiles are identified, and fixed point techniques are developed to predict where profiles pinch in composition space. The first two papers in this series derived and analyzed the fundamental mathematical and geometric properties of difference points for cascade sections (Chem. Eng. Sci. 55(16), 3145) and developed a lever rule to facilitate discovery of full column design alternatives (Chem. Eng. Sci. 55(16), 3161). This third paper provides the analytical basis for identifying reachable feed compositions of reactive cascades. (C) 2004 Elsevier Ltd. All rights reserved.