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In education interventions, the social network within each school provides insight into the mechanisms that affect student outcomes and acts as a powerful mediating variable. Methods to model an intervention on several social networks at once have not been studied until now. Thus, we introduce a new hierarchical modeling framework to model multiple networks and network-level interventions. As an example, we present novel latent space models, a multiple latent space model for observational data and a causal latent space model for experimental interventions. We also introduce methods for estimation and illustrate our estimation algorithm on both real and simulated data. Simulations show that our causal model is able to recover treatment effects even with a relatively small number of networks.