Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the over-all representativeness of the selected set. An unintended consequence of these constraints, however, is reduced in-group fairness: the selected candidates from a given group may not be the best ones, and this unfairness may not be well-balanced across groups. In this paper we study this phenomenon using datasets that comprise multiple sensitive attributes. We then introduce additional constraints, aimed at balancing the in-group fairness across groups, and formalize the induced optimization problems as integer linear programs. Using these programs, we conduct an experimental evaluation with real datasets, and quantify the feasible trade-offs between balance and overall performance in the presence of diversity constraints.