The genotype-phenotype (GP) map describes the association between genetic and phenotypic variation in a biological system. It delimits the phenotypic variation that a system can produce and its accessibility from any given genotype, thus determining the capacity of a system to evolve. The GP map is itself determined by the genetic architecture of the system—the set of rules by which genotype is transformed into phenotype. Deep mutational scanning (DMS) now allows for construction of large empirical GP maps for protein biochemical phenotypes, but studies to date have only studied variation in functions that exist in modern proteins; we still lack a comprehensive understanding of the ability of systems to produce functions that could theoretically exist but are not observed in nature. In this dissertation, I use DMS to interrogate the capacity of the steroid hormone receptor protein to produce specificity for all possible DNA substrates that vary at two functionally important nucleotide sites, most of which are not bound by modern steroid receptors. I perform this experiment in the background of two reconstructed ancestral steroid receptors, allowing me to compare the distribution of outcomes that could have been produced with the phenotypes that evolved in the proteins’ descendants. I then analyze the genetic architecture of this system using a generalized linear modeling framework. I find that the ancestral GP maps were strongly biased in the specificities they were able to produce, and that these biases are congruent with the distribution of specificities seen in their descendants. I also find that the genetic architecture of binding and specificity is largely determined by interactions between individual amino acids and nucleotides. Overall, my work shows how the genetic mechanisms that produce phenotypic variation shaped the evolutionary history of a protein family.