A method for synthesizing separation processes for multicomponent mixtures is presented which identifies the regions, boundaries, and the lower dimensional varieties in an N-dimensional space. Both thermodynamic and equipment boundaries, which may block or limit a proposed separation step, are considered. To facilitate process synthesis, process boundaries are approximated as linear hyperplanes if appropriate, while nonlinear boundaries are represented using a set of linear hyperplanes. In conjunction with the available separation task selection methods, a step-by-step procedure is proposed to generate complete flowsheet alternatives, which allow bypassing both thermodynamic and equipment boundaries to achieve a given separations objective. Several example problems are solved using a spreadsheet program to illustrate the simplicity and applicability of this approach.