In this paper, we consider how fluid teams and fluid tasks interact to affect team performance. We study the effect of diversity in experience on a team's ability to respond to changing tasks by separately examining interpersonal team diversity (i.e., the difference in experience across the entire team) and intrapersonal team diversity (i.e., whether individuals on the team are more or less specialized). We also, examine whether team familiarity - team members' prior experience working with one another - helps teams to cope with the expected challenges created by changing tasks and greater interpersonal team diversity. Using detailed project- and individual-level data from an Indian software services firm, we find that the interaction of task change and intrapersonal diversity is related to improved project performance while the interaction of task change and interpersonal diversity is related to worse project performance. These results suggest that though diverse experience across team members decreases flexibility to change, diverse experience within team members increases flexibility. Additionally, we find that team familiarity partially alleviates the negative effect of interpersonal diversity on two of our three dimensions of project performance. Our results highlight the need for more nuanced approaches to leveraging experience in managing teams.