When a vaccine is not 100% efficacious, there is often interest in intermediate endpoints such as immune response and interest in any differential vaccine effects on different genetic groups of pathogens, or sieve analyses. These aspects of the vaccine's effect aid understanding and can guide future vaccine development. When there is no clear way to define genetic groups of pathogens for a sieve analysis, an immune response that correlates with efficacy can help target the analysis. In addition, a sieve effect based on a particular genetic region can lead to a set of immune responses that are strong correlate candidates. Traditionally, such analyses are run separately. Combining them into a single analysis can improve efficiency and provide clues about the mechanism of vaccine effect. For a particular setting of interest, we derive the expected efficacy gains over a standard correlates of protection analysis and simulations show similar results for more general settings.