Duplication of genes encoding transcription factors plays an essential role in driving phenotypic variation. Because regulation can occur at multiple levels, it is often difficult to discern how each duplicated factor achieves its regulatory specificity. In these cases, a "systems approach" may distinguish the role of each factor by integrating complementary large-scale measurements of the regulatory network. To explore such an approach, we integrate growth phenotypes, promoter binding profiles, and gene expression patterns to model the DNA damage response network controlled by the Yeast-specific AP-1 (YAP) family of transcription factors. This analysis reveals that YAP regulatory specificity is achieved by at least three mechanisms: (i) divergence of DNA-binding sequences into two subfamilies; (ii) condition-specific combinatorial regulation by multiple Yap factors; and (iii) interactions of Yap 1, 4, and 6 with chromatin remodeling proteins. Additional microarray experiments establish that Yap 4 and 6 regulate gene expression through interactions with the histone deacetylase, Hda1. The data further highlight differences among Yap paralogs in terms of their regulatory mode of action (activation vs. repression). This study suggests how other large TF families might be disentangled in the future.