A new design that involves inserting three permeable barriers with negligible thickness to divide a parallel-plate device into four subchannels has been investigated theoretically. The analytical solution has been obtained by using the orthogonal expansion technique with the eigenfunctions expanding in terms of an extended power series. The results are represented graphically and compared with those obtained using a single-pass device (without inserting permeable barriers). Considerable improvement in mass transfer is obtained by employing such a multi-pass device, instead of using the single-pass one. The effects of the subchannel thickness ratio on the mass transfer efficiency enhancement as well as on the increment of power consumption are also been discussed.