Recommender systems often operate on item catalogs clustered by genres, and user bases that have natural clusterings into user types by demographic or psychographic attributes. Prior work on system-wide diversity has mainly focused on defining intent-aware metrics among such categories and maximizing relevance of the resulting recommendations, but has not combined the notions of diversity from the two point of views of items and users. In this work, (1) we introduce two new system-wide diversity metrics to simultaneously address the problems of diversifying the categories of items that each user sees, diversifying the types of users that each item is shown, and maintaining high recommendation quality. We model this as a subgraph selection problem on the bipartite graph of candidate recommendations between users and items. (2) In the case of disjoint item categories and user types, we show that the resulting problems can be solved exactly in polynomial time, by a reduction to a minimum cost flow problem. (3) In the case of non-disjoint categories and user types, we prove NP-completeness of the objective and present efficient approximation algorithms using the submodularity of the objective. (4) Finally, we validate the effectiveness of our algorithms on the MovieLens-1m and Netflix datasets, and show that algorithms designed for our objective also perform well on sales diversity metrics, and even some intent-aware diversity metrics. Our experimental results justify the validity of our new composite diversity metrics.