Causal effect estimation for multiple time-to-event outcomes can be complicated by the issue of semicompeting risks, where a nonterminal event (e.g., hospital readmission) may be truncated by a terminal event (e.g., death). Comment et al. (2019) recently introduced new causal estimands for this setting with accompanying estimators relying on strong parametric assumptions. One goal of causal inference is to detect when treatment should be tailored on the basis of covariates, in which case strong parametric assumptions can be problematic in two ways: inadequacy of confounder adjustment, and inability to characterize heterogeneous treatment effects. To relax these assumptions, we propose a flexible approach using Bayesian additive regression trees (BART), a machine learning ensemble method allowing for higher-order interactions between covariates. The method uses a likelihood factorization to separate BART subcomponent models that can be recombined for estimation of principal stratum causal effects. We demonstrate our approach in the context of estimating time-varying survivor average causal effects for hospital readmission among newly diagnosed late-stage pancreatic cancer patients.