The construction and assembly of artificial allosteric protein switches into information and energy processing networks connected to both biological and non-biological systems is a central goal of synthetic biology and bionanotechnology. However, designing protein switches with the desired input, output and performance parameters is challenging. Here we use a range of reporter proteins to demonstrate that their chimeras with duplicated receptor domains produce YES gate protein switches with large (up to 9,000-fold) dynamic ranges and fast (minutes) response rates. In such switches, the epistatic interactions between largely independent synthetic allosteric sites result in an OFF state with minimal background noise. We used YES gate protein switches based on β-lactamase to develop quantitative biosensors of therapeutic drugs and protein biomarkers. Furthermore, we demonstrated the reconfiguration of YES gate switches into AND gate switches controlled by two different inputs, and their assembly into signalling networks regulated at multiple nodes.