We performed multivariate GWAS, biological annotation, and genetic association analyses using the factors and residual SUD genetic effects identified in our study to address our three main questions related to improving insights into the neurobiology of broad and specific genetic effects on SUD. Our results demonstrate that modeling genetic covariance of SUDs alongside related externalizing traits improves gene discovery for SUDs and did not result in loss of specificity to detect SUD-specific effects. We base this argument on the observation that, across analyses, the broad externalizing factor was better powered to detect genetic variants for and account for variance in SUDs relative to the more specific factors and that analyzing SUDs separately did not result in novel findings related to SUDs.