The proteins associated with gene regulation are often shared between multiple pathways simultaneously. By way of contrast, models in regulatory biology often assume these pathways act independently. We demonstrate a framework for calculating the change in gene expression for the interacting case by decoupling repressor occupancy across the cell from the gene of interest by way of a chemical potential. The details of the interacting regulatory architecture are encompassed in an effective concentration, and thus, a single scaling function describes a collection of gene expression data from diverse regulatory situations and collapses it onto a single master curve.