In high-throughput functional genomic screens, each gene product is commonly assumed to exhibit a singular biological function within a defined protein complex or pathway. In practice, a single gene perturbation may induce multiple cascading functional outcomes, a genetic principle known as pleiotropy. Here, we model pleiotropy in fitness screen collections by representing each gene perturbation as the sum of multiple perturbations of biological functions, each harboring independent fitness effects inferred empirically from the data. Our approach (Webster) recovered pleiotropic functions for DNA damage proteins from genotoxic fitness screens, untangled distinct signaling pathways upstream of shared effector proteins from cancer cell fitness screens, and predicted the stoichiometry of an unknown protein complex subunit from fitness data alone. Modeling compound sensitivity profiles in terms of genetic functions recovered compound mechanisms of action. Our approach establishes a sparse approximation mechanism for unraveling complex genetic architectures underlying high-dimensional gene perturbation readouts.