Engineering the antibody Fc region to enhance the cytotoxic activity of therapeutic antibodies is currently an active area of investigation. The contribution of complement to the mechanism of action of some antibodies that target cancers and pathogens makes a compelling case for its optimization. Here we describe the generation of a series of Fc variants with enhanced ability to recruit complement. Variants enhanced the cytotoxic potency of an anti-CD20 antibody up to 23-fold against tumor cells in CDC assays, and demonstrated a correlated increase in C1q binding affinity. Complement-enhancing substitutions combined additively, and in one case synergistically, with substitutions previously engineered for improved binding to Fc gamma receptors. The engineered combinations provided a range of effector function activities, including simultaneously enhanced CDC, ADCC, and phagocytosis. Variants were also effective at boosting the effector function of antibodies targeting the antigens CD40 and CD19, in the former case enhancing CDC over 600-fold, and in the latter case imparting complement-mediated activity onto an IgG1 antibody that was otherwise incapable of it. This work expands the toolkit of modifications for generating monoclonal antibodies with improved therapeutic potential, and enables the exploration of optimized synergy between Fc gamma receptors and complement pathways for the destruction of tumors and infectious pathogens.