We interrogate the joint genetic architecture of 11 major psychiatric disorders at biobehavioral, functional genomic and molecular genetic levels of analysis. We identify four broad factors (neurodevelopmental, compulsive, psychotic and internalizing) that underlie genetic correlations among the disorders and test whether these factors adequately explain their genetic correlations with biobehavioral traits. We introduce stratified genomic structural equation modeling, which we use to identify gene sets that disproportionately contribute to genetic risk sharing. This includes protein-truncating variant-intolerant genes expressed in excitatory and GABAergic brain cells that are enriched for genetic overlap across disorders with psychotic features. Multivariate association analyses detect 152 (20 new) independent loci that act on the individual factors and identify nine loci that act heterogeneously across disorders within a factor. Despite moderate-to-high genetic correlations across all 11 disorders, we find little utility of a single dimension of genetic risk across psychiatric disorders either at the level of biobehavioral correlates or at the level of individual variants.