Complex traits are challenging to study because there are numerous underlying genetic factors, interactions between genes and the environment, and interactions between the traits themselves. In the yeast Saccharomyces cerevisiae, two important complex traits – invasive growth and sexual reproduction – rely on a single transcription factor, Ste12, for proper expression. We used deep mutational scanning to examine the interaction between these complex traits by analyzing single amino acid perturbations in the DNA-binding domain of Ste12. Because alternative modes of DNA binding are implicated in the diverse functions of Ste12, we focused on a critical segment of the protein that is likely to contact DNA. By selecting for the ability of yeast either to invade or to mate, we sought to find sites in the protein needed either for both traits equally or for one at the expense of the other. We identified residues within the DNA-binding domain of Ste12 that could not be mutated without loss of mating, while mutations at these same positions still allowed invasion. In fact, some mutations even increased the ability of cells to invade at the cost of mating, revealing that a trade-off between invasion and sexual reproduction is encoded within a short segment of Ste12’s DNA-binding domain. To explore the role of the environment, we identified mutations that increase the dependence of mating on temperature. We found that temperature-dependent variation overlaps with Hsp90-dependent variation, implying that Ste12’s DNA-binding function may be stabilized by chaperones. Given the role of Ste12 as the ultimate recipient of diverse signals and the results of our mutational analysis, we suggest that flexibility in DNA-binding may be critical to Ste12 function. These findings increase our understanding of the interactions between complex traits, while also revealing a possible mechanism for the evolutionarily conserved link between invasion and sexual reproduction.