Advances in high-performance computing have led to the broad use of computational studies in everyday engineering and scientific applications. A single study may require thousands of computational experiments, each corresponding to individual runs of simulation software with different parameter settings; in complex studies, the pattern of parameter changes is complex and may have to be adjusted by the user based on partial simulation results. Unfortunately, existing tools have limited high-level support for managing large ensembles of simultaneous computational experiments. In this paper, we present a system architecture for interactive computational studies targeting two goals. The first is to provide a framework for high-level user interaction with computational studies, rather than individual experiments; the second is to maximize the size of the studies that can be performed at close to interactive rates. We describe a prototype implementation of the system and demonstrate performance improvements obtained using our approach for a simple model problem.