A network flow model is presented for synthesizing crystallization-based separations for multicomponent systems. The construction of the network flow is based on the identification of feasible thermodynamic states. The method allows consideration of several operation temperatures, complex solid-liquid equilibrium behavior, and several multicomponent feeds and products. For systems with two solutes a linear programming model is obtained, while for systems with three or more solutes a nonlinear programming model is obtained. The relative composition diagram is proposed to determine feasible operation points. For a small problem the relative composition diagram can be used to recognize flowsheet alternatives. For large problems, the relative composition diagram allows one to decrease the nodes in the network, thus decreasing the execution time. The technique is illustrated with three example problems.