In this article we study the extent to which the interplay between recommended items affect recommendation effectiveness. We introduce and formalize the concept of co‐utility as the property that any pair of recommended items has of being useful to a user, and exploit it to improve collaborative filtering recommendations. We present different techniques to estimate co‐utility probabilities, all of them independent of content information, and compare them with each other. We use these probabilities, as well as normalized predicted ratings, in an instance of an NP‐hard problem termed the Max‐Sum Dispersion Problem (MSDP). A solution to MSDP hence corresponds to a set of items for recommendation. We study one heuristic and one exact solution to MSDP and perform comparisons among them. We also contrast our solutions (the best heuristic to MSDP) to different baselines by comparing the ratings users give to different recommendations. We obtain expressive gains in the utility of recommendations and our solutions also recommend higher‐rated items to the majority of users. Finally, we show that our co‐utility solutions are scalable in practice and do not harm recommendations' diversity.