We generalize the computation of the Regulatory Potential (RP) score from two-way alignments of human and mouse to three-way alignments of human, mouse, and rat. This requires overcoming technical challenges that arise because the complexity of the models underlying the score increases exponentially with the number of species. Despite the close evolutionary proximity of rat to mouse, we find that adding the rat sequence increases our ability to predict genomic sites that regulate gene transcription. A variant of the RP scoring scheme that accounts for local variation in neutral mutational patterns further improves our predictions.