A crucial concern of toxicologists is to determine an acceptable exposure level(s) to a hazardous substance(s). Often lab experiments produce data featuring multiple hazards and multiple outcome measures. The current practice evaluates each hazard and outcome combination separately, which leads to multiple statistical tests that suffer from inflated Type I error rates. This paper introduces a Bayesian model-based approach for analyzing data of similar nature. This approach is dimension-preserving in that it permits simultaneous quantification of an acceptable exposure level among multiple hazards. Furthermore, we introduce the concept of significance probabilities to assess the importance of the outcomes in determining an acceptable exposure level. The proposed methodology is motivated and illustrated through analyzing the dataset from a rodent study of pesticides on neurotoxicity conducted by Moser et al. (2005).