The systematic generation of process alternatives for multicomponent heterogeneous or homogeneous distillation systems is described. Alternatives based on distillation and decanting alone must generally be expanded by mixing and occasionally by recycling to provide high-purity products. For azeotropic mixtures, systematic considerations of recycles further expand those alternatives to meet the additional goal of high recoveries. The latter generates many potential alternatives, and new necessary conditions given here for feasible recycle destinations eliminate as many as 90% of the infeasible alternatives without the need for a complete converged material balance simulation. The physical meaning of this recycle reachability rule is that there must be an exit point for each component not only for the entire process system, but also within each recycle loop. The recycling of pure components is also identified as a useful and sometimes essential feature in developing alternatives. Selected results are reported for a ternary mixture of ethanol, benzene, and water and also for a quaternary mixture of water, n-butanol, acetic acid, and n-butyl acetate.