Cell signals often act to ultimately affect the transcription of genes, and it is common for twodifferent signals to affect the transcription of the same gene. In such cases, it is natural to ask how the combined transcriptional response compares to the individual responses. Mechanistic models can predict a range of combined responses, with the most commonly applied models predicting additive or multiplicative responses, but systematic genome-wide evaluation of these predictions have not been available. Here, we performed a comprehensive analysis of the transcriptional response of human MCF-7 cells to two different signals (retinoic acid and TGF-β), applied individually and in combination. We found that the combined responses exhibited a range of behaviors, but clearly favored both additive and multiplicative combined transcriptional responses. We also performed paired chromatin accessibility measurements, which previously have been shown to correlate with transcription factor occupancy at DNA regulatory elements. We found that increases in chromatin accessibility were largely additive, meaning that the accessibility response was the sum of the accessibility responses to each signal individually. We found some association between super-additivity of accessibility and multiplicative or super-multiplicative combined transcriptional responses, while sub-additivity of accessibility associated with additive transcriptional responses. For peaks that experienced increases in accessibility, there was a modest increase in the likelihood of a peak to be super-additive when it contained both a retinoic acid-associated transcription factor motif and a TGF-β-associated transcription factor motif. Our findings suggest that mechanistic models of combined transcriptional regulation must be able to reproduce a range of behaviors.