Determining proper sensitivity to incoming signals is fundamental to all regulated biological responses, but how thresholds are established within eukaryotic signal transduction networks is not understood. Here, we approach this question using chemical biology and single-cell western blotting, and then verify our conclusions with mathematical modeling. Focusing on the bistable kinase network that governs progesterone-induced meiotic entry in Xenopus oocytes, we characterize glycogen-synthase kinase-3&beta (GSK-3&beta) as a dampener of progesterone sensitivity. GSK-3&beta engages the meiotic kinase network through a double-negative feedback loop; this specific feedback architecture raises oocytes' progesterone threshold in proportion to the strength of double-negative signaling. These data demonstrate that intracellular signaling nodes can tune a system's response threshold away from the basal EC50 established by ligand-receptor interactions. Because oocytes actively depress their progesterone sensitivity, they can integrate additional signals into their decision to enter meiosis, an impossibility if they were maximally sensitive to one stimulus. Accordingly, we identify the branched-chain amino acid L-Leucine as a natural, sensitizing co-stimulus and show that an oocyte's native progesterone threshold can be lowered under specific nutrient conditions. In a chemical biology experiment that is conceptually similar to genetic epistasis, we show that L-Leucine adjusts oocytes' progesterone thresholds in a GSK-3&beta-dependent manner.