Chemogenetic regulators of transgene activity, such as the tetracycline-inducible system derived from the tetracycline resistance operon of the bacterial transposon Tn10, are critical and widely used systems in cellular engineering. The tetracycline-inducible system is prized for its selectivity, high affinity, inducibility, reversibility, and differential control of gene transcription. However, its optimization for binary on/off expression limits its application in systems biology and the modeling and construction of complex regulatory systems with intricate input/output paradigms. To overcome this limitation, we developed a high-throughput reporter system to investigate a saturated mutagenesis library of tetracycline resistance operator variants. Using this system, we mapped the functional interactions of Tet repressor DNA binding protein at single-nucleotide resolution in mammalian cells. Our comprehensive screen revealed a spectrum of variant effects, ranging from a nearly complete loss of repression to levels indistinguishable from the natural operator, validated through orthogonal assays. This comprehensive characterization of the sequence-specificity of a tetracycline resistance operator facilitates the construction of variably suppressive, inducible systems for dynamic and modular control over gene expression in mammalian cell culture.