Several abilities outside literacy proper are associated with reading and spelling, both phenotypically and genetically, though our knowledge of multivariate genomic covariance structures is incomplete. Here, we introduce structural models describing genetic and residual influences between traits to study multivariate links across measures of literacy, phonological awareness, oral language, and phonological working memory (PWM) in unrelated UK youth (8-13 years, N=6,453). We find that all phenotypes share a large proportion of underlying genetic variation, although especially oral language and PWM reveal substantial differences in their genetic variance composition with substantial trait-specific genetic influences. Multivariate genetic and residual trait covariance showed concordant patterns, except for marked differences between oral language and literacy/phonological awareness, where strong genetic links contrasted near-zero residual overlap. These findings suggest differences in etiological mechanisms, acting beyond a pleiotropic set of genetic variants, and implicate variation in trait modifiability even among phenotypes that have high genetic correlations.