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This paper reports a method to control the fluid flow in paper-based microfluidic devices simply by pressing over the channel surface of paper, thereby decreasing the pore size and permeability of a non-woven polypropylene sheet. As a result, fluid resistance is increased in the pressed region and causes flow rate to decrease. We characterize the decrease of flow rate with respect to different amounts of pressure applied, and up to 740% decrease in flow velocity was achieved. In addition, we demonstrate flow rate control in a Y-shaped merging paper and sequential delivery of multiple color dyes in a three-branched paper. Furthermore, sequential delivery of multiple fluid samples is performed to demonstrate its application in multi-step colorimetric immunoassay, which shows a 4.3-fold signal increase via enhancement step.