Motivated by the prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have non-additive preferences over combinations. We establish non-parametric identification of primitives in this model under standard exclusion restrictions, providing a basis for both estimation and testing of preferences over combinations. We then apply our model to data on Michigan Department of Transportation (MDOT) highway procurement auctions, quantifying the magnitude of cost synergies and evaluating the performance of the simultaneous first-price mechanism in the MDOT marketplace.