Heterogeneous treatment effect estimation is an important problem in precision medicine. Specific interests lie in identifying the differential effect of different treatments based on some external covariates. We propose a novel non-parametric treatment effect estimation method in a multi-treatment setting. Our non-parametric modeling of the response curves relies on radial basis function (RBF)-nets with shared hidden neurons. Our model thus facilitates modeling commonality among the treatment outcomes. The estimation and inference schemes are developed under a Bayesian framework using thresholded best linear projections and implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of the analysis. The numerical performance of the method is demonstrated through simulation experiments. Applying our proposed method to MIMIC data, we obtain several interesting findings related to the impact of different treatment strategies on the length of ICU stay and 12-hour SOFA score for sepsis patients who are home-discharged.