Cellular signaling networks coordinate physiological processes in all multicellular organisms. Within networks, modules switch their function to control signaling activity in response to the cellular context. However, systematic approaches to map the interplay of such modules have been lacking. Here, we generated a context-dependent genetic interaction network of a metazoan's signaling pathway. Using Wnt signaling in Drosophila as a model, we measured >290,000 double perturbations of the pathway in a baseline state, after activation by Wnt ligand or after loss of the tumor suppressor APC. We found that genetic interactions within the Wnt network globally rewired after pathway activation. We derived between-state networks that showed how genes changed their function between state-specific networks. This related pathway inhibitors across states and identified genes required for pathway activation. For instance, we predicted and confirmed the ER-resident protein Catsup to be required for ligand-mediated Wnt signaling activation. Together, state-dependent and between-state genetic interaction networks identify responsive functional modules that control cellular pathways.