Understanding the relationships between chemical exposure and cancer incidence is an important probable in environmental epidemiology. Individually, each pesticide might transmit small amounts of risk, but taken together, may pose substantial cancer risk. Importantly, these effects can be highly non-linear and can be in different directions. We develop an approach that models the simultaneous effect of all chemicals as the sum of nonlinear functions of each chemical. Since it is highly probable that many chemicals transmit small amounts of risk, and only taken together would we anticipate a sizable effect, we do not use traditional model selection approaches such as LASSO. Instead, we propose an approach in which individual effects are modeled as mixtures of non-linear functions to characterize the simultaneous effects of many different agents. We use state-of-the-art Bayesian methodology to estimate models with potentially large number of mixtures and use penalized likelihood approaches to choose an appropriate number of nonlinear functions. We illustrate this methodology with data from cohort studies trying to address this important public health issues.