We previously identified a highly active homodimeric FMN-dependent NADH-preferred azoreductase (AzoA) from Enterococcus faecalis, which cleaves the azo bonds (R-N˭N-R) of diverse azo dyes, and determined its crystal structure. The preliminary network-based mutational analysis suggested that the two residues, Arg-21 and Asn-121, have an apparent mutational potential for fine-tuning of AzoA, based on their beneficial pleiotropic feedbacks. However, epistasis between the two promising mutational spots in AzoA has not been obtained in terms of substrate binding and azoreductase activity. In this study, we further quantified, visualized, and described the pleiotropic and/or epistatic behavior of six single or double mutations at the positions, Arg-21 and Asn-121, as a further research endeavor for beneficial fine-tuning of AzoA. Based on this network-based mutational analysis, we showed that pleiotropy and epistasis are common, sensitive, and complex mutational behaviors, depending mainly on the structural and functional responsibility and the physicochemical properties of the residue(s) in AzoA.