A generalized approach for the conceptual design of complex distillation columns including multiple-feed/side stream columns and columns with side sections is presented. The new design approach assumes constant relative volatility mixtures and constant molar flow rates within each column section. Furthermore, it is based on the identification of all possible constant composition zones in a column including those around the feed sections and those around the side stream sections. Each set of constant composition zones is characterized by the relevant mass transfer sections along with the respective Eigenfunctions and split. Accordingly, new design algorithms are proposed for rapid and accurate calculation of all relevant design parameters at pinch conditions for all studied complex column configurations separating ideal behaving multicomponent mixtures. For mixtures with up to four components, separation geometries of complex distillation columns are established; allowing thereby the analysis of the geometric properties of such complex columns. Finally, it is shown that the developed algorithms can be successfully applied to providing good estimates of design parameters for complex distillation columns separating highly non ideal azeotropic mixtures, after approximating the latter by appropriate constant relative volatility pseudo-ideal mixtures. (c) 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.