Abstract: To meet regulatory approval, pharmaceutical companies often must demonstrate that new vaccines reduce the total risk of a post-infection outcome like transmission, symptomatic disease, or severe illness in randomized, placebo-controlled trials. Given that infection is necessary for a postinfection outcome, one can use principal stratification to partition the total causal effect of vaccination into two causal effects: vaccine efficacy against infection, and the principal effect of vaccine efficacy against a post-infection outcome in always-infected patients. Despite the importance of such principal effects to policymakers, these estimands are generally unidentifiable, even under strong assumptions that are rarely satisfied in real-world trials. We develop a novel method to nonparametrically point identify these principal effects while eliminating the monotonicity assumption and allowing for measurement error. Moreover, our results readily generalize to multiple treatments. Our method relies on the fact that many vaccine trials are multi-center trials, and measure biologically-relevant categorical pretreatment covariates. We show our method can be used to design clinical trials where vaccine efficacy against infection and a post-infection outcome can be jointly inferred. This methodology can yield new insights from existing vaccine efficacy trial data and will aid researchers in designing new multi-arm clinical trials.