A multipass mass exchanger through a parallel-plate channel by inserting three permeable barriers with uniform wall concentration was designed and the mathematical formulation was investigated for solving such a conjugated Graetz problem by using an orthogonal expansion technique. Considerable improvement in the mass-transfer efficiency is obtainable by such multipass operations with suitable adjustment of the permeable-barrier locations. Comparisons of analytical results have shown that the multipass device can enhance the mass-transfer efficiency compared with those of the single-pass (without permeable barrier inserted) and double-pass operations of the same size in the previous work. The ratio of the improvement of transfer efficiency to the increment of power consumption has been determined to make good economic sense.