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Paper-based electrochemical biosensors are a promising technology that enables rapid, quantitative measurements on an inexpensive platform. However, the control of liquids in paper networks is generally limited to a single sample delivery step. Here, we propose a simple method to automate the loading and delivery of liquid samples to sensing electrodes on paper networks by stacking multiple layers of paper. Using these stacked paper devices (SPDs), we demonstrate a unique strategy to fully immerse planar electrodes by aqueous liquids via capillary flow. Amperometric measurements of xanthine oxidase revealed that electrochemical sensors on four-layer SPDs generated detection signals up to 75% higher compared with those on single-layer paper devices. Furthermore, measurements could be performed with minimal user involvement and completed within 30 min. Due to its simplicity, enhanced automation, and capability for quantitative measurements, stacked paper electrochemical biosensors can be useful tools for point-of-care testing in resource-limited settings.