Process design and simulation of multi-stage membrane systems have been widely studied in many gas separation systems. However, general guidelines have not been developed yet for the attainability and the minimum energy consumption of a multi-stage membrane system. Such information is important for conceptual process design and thus it is the topic of this work. Using a well-mixed membrane model, it was determined that the attainability curve of multi-stage systems is defined by the pressure ratio and membrane selectivity. Using the constant recycle ratio scheme, the recycle ratio can shift the attainability behavior between single-stage and multi-stage membrane systems. When the recycle ratio is zero, all of the multi-stage membrane processes will decay to a single-stage membrane process. When the recycle ratio approaches infinity, the required selectivity and pressure ratio reach their absolute minimum values, which have a simple relationship with that of a single-stage membrane process, as follows: Sn=S1, γn=γ1, where n is the number of stages. The minimum energy consumption of a multi-stage membrane process is primarily determined by the membrane selectivity and recycle ratio. A low recycle ratio can significantly reduce the required membrane selectivity without substantial energy penalty. The energy envelope curve can provide a guideline from an energy perspective to determine the minimum required membrane selectivity in membrane process designs to compete with conventional separation processes, such as distillation.