Five novel internally staged permeator (ISP) designs for membrane-based gas separations are described. Two permeate streams, a low-pressure and an intermediate-pressure permeate, and a high-pressure retenate stream are produced in an ISP. Three of the new designs utilize a woven fabric or alternating sheets of fibers to enable contacting patterns that are not possible with previous designs. All designs are compared for the production of an enriched oxygen permeate from air. Design and operational parameters were selected to maximize the recovery of the enriched oxygen product. Of the new designs,the best performer is the co-cross design. The best overall performer is the co-counter design. The co-cross design is able to recover 33% of the feed as a 42% oxygen permeate while the co-counter design is able to recover 35% of the feed in contrast to the 12% recovery provided by a single countercurrent stage. However, this increase in recovery comes at the expense of a significant increase in required membrane area: the co-cross design requires 20x more area than the countercurrent stage while the co-counter design requires 23x more area. All ISP designs are capable of producing higher permeate purities than achievable in a single countercurrent stage. The co-counter design can recover 12% of the feed as a 52% oxygen permeate while a single countercurrent stage is limited to purities less than 45%.