A major goal of public health research is to assess the risk posed by mixtures of environmental exposures. Two popular approaches for mixtures analyses are response-surface methods and exposure-index methods. The former estimate high-dimensional surfaces and are highly flexible but difficult to interpret. The latter decompose a linear model into an overall mixture effect and index weights; these are highly interpretable and efficient but can be overly restrictive. We propose a Bayesian multiple index model framework to combine the strengths of each, allowing for non-linear and non-additive relationships among exposure indices, while estimating index weights with variable selection. The framework contains a spectrum of models ranging from exposure-index models to response surface models, allowing one to select an analysis with an appropriate balance of flexibility and interpretability. The proposed framework also provides a means of incorporating prior knowledge about mixtures.