Algorithmic fairness in recommender systems requires close attention to the needs of a diverse set of stakeholders that may have competing interests. Previous work in this area has often been limited by fixed, single-objective definitions of fairness, built into algorithms or optimization criteria that are applied to a single fairness dimension or, at most, applied identically across dimensions. These narrow conceptualizations limit the ability to adapt fairness-aware solutions to the wide range of stakeholder needs and fairness definitions that arise in practice. Our work approaches recommendation fairness from the standpoint of computational social choice, using a multi-agent framework. In this paper, we explore the properties of different social choice mechanisms and demonstrate the successful integration of multiple, heterogeneous fairness definitions across multiple data sets.