Approaches for estimating the causal effects of a binary treatment have been well documented. Causal effect estimation with multiple treatments, meanwhile, requires additional assumptions and more refined techniques. We demonstrate the usefulness of Bayesian Additive Regression Trees (BART) in these settings. Among its advantages, BART is straightforward to implement, requires fewer user inputs, and operates smoothly with large numbers of covariates. We explore the operating characteristics of BART with multiple treatments, and use simulations to compare BART to alternative approaches, including matching on vectors of generalized propensity scores and inverse probability weighting. We conclude by using each approach to estimate the causal effects of three surgical options available to non-smell-cell lung cancer patients.