Motivated by a real example of understanding the so-called "building related occupant complaint syndromes" (BROCS), we propose a tree-based method for analyzing a multivariate ordinal response. Our method is semiparametric by assuming a within-node parametric distribution on the adaptive nonparametric tree framework. We use simulation experiments to demonstrate the ability of our method to identify underlying structures in the data and the fact that analyzing ordinal response data with proper methods that take ordinality into account is considerably more powerful than dichotomization. The reanalysis of the BROCS data also suggests new insights that go beyond a previous analysis based on the dichotomization.