Neutral mutational drift is an important source of biological diversity that remains underexploited in fundamental studies of protein biophysics. This study uses a synthetic transcriptional circuit to study neutral drift in protein tyrosine phosphatase 1B (PTP1B), a mammalian signaling enzyme for which conformational changes are rate limiting. Kinetic assays of purified mutants indicate that catalytic activity, rather than thermodynamic stability, guides enrichment under neutral drift, where neutral or mildly activating mutations can mitigate the effects of deleterious ones. In general, mutants show a moderate activity‐stability tradeoff, an indication that minor improvements in the activity of PTP1B do not require concomitant losses in its stability. Multiplexed sequencing of large mutant pools suggests that substitutions at allosterically influential sites are purged under biological selection, which enriches for mutations located outside of the active site. Findings indicate that the positional dependence of neutral mutations within drifting populations can reveal the presence of allosteric networks and illustrate an approach for using synthetic transcriptional systems to explore these mutations in regulatory enzymes.