In this paper, we introduce the parallel composition of Constraint Automata (CA), a variant of the original composition of Constraint Automata better suited to compactly represent highly concurrent compositional models, such as Reo. By relegating the crux of composition to run-time, our parallel composition maintains the integrity of the constituent parts of a composite model, allowing dynamic modification of CA models. We discuss the run-time structure of the parallel composition with its implementation in Maude, and the notion of maximality for a composite transition with respect to various criteria. We show the utility of parallel composition in formal analysis through Maude search queries.