There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian additive regression trees in such settings. First, we compare Bayesian additive regression trees to several approaches that have been proposed for continuous outcomes, including inverse probability of treatment weighting, targeted maximum likelihood estimator, vector matching, and regression adjustment. Results suggest that under conditions of non-linearity and non-additivity of both the treatment assignment and outcome generating mechanisms, Bayesian additive regression trees, targeted maximum likelihood estimator, and inverse probability of treatment weighting using generalized boosted models provide better bias reduction and smaller root mean squared error. Bayesian additive regression trees and targeted maximum likelihood estimator provide more consistent 95% confidence interval coverage and better large-sample convergence property. Second, we supply Bayesian additive regression trees with a strategy to identify a common support region for retaining inferential units and for avoiding extrapolating over areas of the covariate space where common support does not exist. Bayesian additive regression trees retain more inferential units than the generalized propensity score-based strategy, and shows lower bias, compared to targeted maximum likelihood estimator or generalized boosted model, in a variety of scenarios differing by the degree of covariate overlap. A case study examining the effects of three surgical approaches for non-small cell lung cancer demonstrates the methods.