Genome-wide association studies (GWAS) are now a common tool among human geneticists to identify genetic variants that significantly affect traits of interest. To date, the NHGRI GWAS Catalog has over 24,000 SNP-phenotype associations. However, the vast majority of these GWAS are conducted in univariate frameworks, ie when genetic variants are only tested against a single phenotype one at a time. This is in contrast to multivariate frameworks where genetic variants are tested against different combinations of traits simultaneously. Multivariate frameworks are of interest because it is well known that under certain biological scenarios these approaches significantly increase power. Additionally, by testing combinations of traits, researchers are able to investigate more complex biological hypotheses. Despite these clear advantages though, there are often recurring reasons why multivariate analyses are not conducted. Univariate GWAS already involve a large computational and statistical burden; performing an extra, exponentially greater number of tests appears highly intractable. Furthermore, it is often unclear how to properly compare different multivariate models even when they can be efficiently conducted. Here, we present a framework and R package that aims to alleviate these obstacles -- Bayesian multivariate analysis of association studies, or bmass. bmass runs on univariate GWAS summary statistics and can quickly conduct all possible multivariate analyses given a set of up to 8 phenotypes. bmass also provides Bayes factors for each multivariate analysis, thus allowing models to be directly compared. Running bmass on various publicly available GWAS datasets consistently show an increase in power up to 40% over univariate approaches while keeping FDRs as low as 15%. bmass also provides novel biological insight at a more intricate level than previously seen, revealing phenotypic combinations that often drive signals of genetic associations. Overall, bmass is a powerful and tractable tool that now allows researchers to effectively conduct multivariate GWAS.