Adaptive enrichment designs involve preplanned rules for modifying enrollment criteria based on accrued data in an ongoing trial. For example, enrollment of a subpopulation where there is sufficient evidence of treatment efficacy, futility, or harm could be stopped, while enrollment for the remaining subpopulations is continued. We propose a new class of multiple testing procedures tailored to adaptive enrichment designs. The procedures synthesize ideas from two general approaches. As in the modified group sequential approach, the procedures gain power by leveraging the covariance among statistics for different stages and different hypotheses. As in the alpha reallocation approach, the procedures lower rejection thresholds for the remaining null hypotheses after others have been rejected. The proposed procedures are proved to have power greater than or equal to several existing methods, and to strongly control the familywise Type I error rate when statistics are normally distributed. The methods are illustrated through simulations of a trial for a surgical intervention for stroke, involving two subpopulations.