The identification of a new generation of potent broadly neutralizing HIV-1 antibodies (bnAbs) has generated substantial interest in their potential use for the prevention and/or treatment of HIV-1 infection. While combinations of bnAbs targeting distinct epitopes on the viral envelope (Env) will likely be required to overcome the extraordinary diversity of HIV-1, a key outstanding question is which bnAbs, and how many, will be needed to achieve optimal clinical benefit. We assessed the neutralizing activity of 15 bnAbs targeting four distinct epitopes of Env, including the CD4-binding site (CD4bs), the V1/V2-glycan region, the V3-glycan region, and the gp41 membrane proximal external region (MPER), against a panel of 200 acute/early clade C HIV-1 Env pseudoviruses. A mathematical model was developed that predicted neutralization by a subset of experimentally evaluated bnAb combinations with high accuracy. Using this model, we performed a comprehensive and systematic comparison of the predicted neutralizing activity of over 1,600 possible double, triple, and quadruple bnAb combinations. The most promising bnAb combinations were identified based not only on breadth and potency of neutralization, but also other relevant measures, such as the extent of complete neutralization and instantaneous inhibitory potential (IIP). By this set of criteria, triple and quadruple combinations of bnAbs were identified that were significantly more effective than the best double combinations, and further improved the probability of having multiple bnAbs simultaneously active against a given virus, a requirement that may be critical for countering escape in vivo. These results provide a rationale for advancing bnAb combinations with the best in vitro predictors of success into clinical trials for both the prevention and treatment of HIV-1 infection.