How cellular and organismal complexity emerges from combinatorial expression of genes is a central question in biology. High-content phenotyping approaches such as Perturb-seq (single-cell RNA-sequencing pooled CRISPR screens) present an opportunity for exploring such genetic interactions (GIs) at scale. Here, we present an analytical framework for interpreting high-dimensional landscapes of cell states (manifolds) constructed from transcriptional phenotypes. We applied this approach to Perturb-seq profiling of strong GIs mined from a growth-based, gain-of-function GI map. Exploration of this manifold enabled ordering of regulatory pathways, principled classification of GIs (e.g., identifying suppressors), and mechanistic elucidation of synergistic interactions, including an unexpected synergy between CBL and CNN1 driving erythroid differentiation. Finally, we applied recommender system machine learning to predict interactions, facilitating exploration of vastly larger GI manifolds.