A new criterion for establishing staged-column feasibility is proposed. The use of 'stage-composition lines' complements existing methods. The intersection of a pair of stage-composition lines is a necessary and sufficient condition for staged-distillation column feasibility. Stage-composition lines can be extended to describe non-ideal column operation as well as packed columns. Every intersection of a set of rectifying and stripping stage-composition lines is an exact converged solution, and produces accurate column specifications where shortcut methods fail. A retrofit method for increasing throughput is developed using stage-composition lines.