AbstractGenetic pleiotropy is when a single gene influences more than one trait. Detecting pleiotropy and understanding its causes can improve the biological understanding of a gene in multiple ways, yet current multivariate methods to evaluate pleiotropy test the null hypothesis that none of the traits are associated with a variant; departures from the null could be driven by just one associated trait. A formal test of pleiotropy should assume a null hypothesis that one or no traits are associated with a genetic variant. For the special case of two traits, one can construct this null hypothesis based on the intersection-union (IU) test, which rejects the null hypothesis only if the null hypotheses of no association for both traits are rejected. To allow for more than two traits, we developed a new likelihood-ratio test for pleiotropy. We then extended the testing framework to a sequential approach to test the null hypothesis that k+1 traits are associated, given that the null of k traits are associated was rejected. This provides a formal testing framework to determine the number of traits associated with a genetic variant, while accounting for correlations among the traits. By simulations, we illustrate the type I error rate and power of our new methods; describe how they are influenced by sample size, the number of traits, and the trait correlations; and apply the new methods to multivariate immune phenotypes in response to smallpox vaccination. Our new approach provides a quantitative assessment of pleiotropy, enhancing current analytic practice.