Group-formation experiments, in which experimental units are randomly assigned to groups, are a powerful tool for studying peer effects in the social sciences. Existing design and analysis approaches allow researchers to draw inference from such experiments without relying on parametric assumptions. In practice, however, group-formation experiments are often coupled with a second, external intervention, that is not accounted for by standard nonparametric approaches. This note shows how to construct Fisherian randomization tests and Neymanian asymptotic confidence intervals for such composite experiments, including in settings where the second intervention exhibits spillovers. We also propose an approach for designing optimal composite experiments.