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Many proteins function as switches, transducing the concentrations of environmental chemicals into cellular responses. It is not well understood how signal processing by switches is genetically encoded. Here, using a massively parallel approach, GluePCA, we present >40,000 measurements and a complete map of how mutations alter the quantitative activation function of a receptor switch, the plant hormone sensor PYL1. Close to 90% of missense variants tune the dose-response of the receptor, often causing correlated changes in sensitivity, basal activity, maximum response and induction steepness. Based on theory we predict and then validate the underlying latent mechanism as a change in protein stability. Beyond this, signalling parameters can be independently tuned, with large effects in interface-distal positions and a modular genetic architecture across the receptor’s structure. Rare single amino acid substitutions confer phenotypic innovation, including inverted and band-stop activation functions. Our data demonstrate the feasibility of dose-response profile quantification at massive scale and reveal the remarkable evolutionary malleability of a protein switch. How mutations shape signal processing in protein switches is not well defined. Here, the authors use GluePCA to profile thousands of PYL1 variants, uncovering modular control of sensitivity, basal activity and maximal response, novel inverter and band-stop mutations, and identifying stability‑driven mechanisms.