The adsorption separation of a multicomponent mixture in a four-section countercurrent separation unit is analyzed. A procedure for the optimal and robust design of the unit is developed in the frame of equilibrium theory, where adsorption equilibria are described through the constant selectivity stoichiometric model, while mass-transfer resistances and axial dispersion are neglected. A set of conditions obtained defines a region in the operating parameters space where the unit achieves complete separation. In the case of binary separations, with a desorbent having any adsorptivity with respect to the components to be separated, the boundaries of this region are obtained explicitly. In the general multicomponent case, a numerical procedure is needed. An approximate shortcut method devised allows to obtain explicit and reliable relationships for estimating the boundaries of the exact region. The results provide a very convenient fool not only to analyze the role of the desorbent in determining the separation performance, but to find both optimal and robust operating conditions. Comparison between model predictions and experimental data assesses the reliability and accuracy of the theoretical findings.