Polygenic scores are imperfect measures of the additive genetic effects of common genetic variants. The resulting measurement error biases estimates of quantities of interest in epidemiological analyses integrating polygenic scores. For example, how much of an exposure-outcome association is genetically confounded can be substantially underestimated when using polygenic scores alone. Here we present extensions to Gsens, a genetic sensitivity analysis, which aims to correct for such measurement error using both polygenic scores and heritability estimates. Gsens now allows for multiple exposures and estimates several quantities of interest, i.e. genetic confounding, adjusted residual association (net of genetic confounding), genetic overlap and environmentally mediated genetic effects. We present derivations and simulations showing how Gsens accounts for measurement error in the polygenic score; we also show how estimation may be affected by misspecifications of the causal structure between exposures. Applying Gsens in the Norwegian Mother, Father and Child Cohort Study (MoBa), we uncover, among other results, substantial genetic confounding in the associations between multiple known risk factors for attention deficit hyperactivity disorder (ADHD), such as low birth weight and temperament, and measures of ADHD in childhood. The updated Gsens R package offers multiple options, including for missing data handling and customisable syntax. Our extended version of Gsens is applicable to a broad range of substantive questions in multiple disciplines.