Data heterogeneity across participating devices poses one of the main challenges in federated learning as it has been shown to greatly hamper its convergence time and generalization capabilities. In this work, we address this limitation by enabling personalization using multiple user-centric aggregation rules at the parameter server. Our approach potentially produces a personalized model for each user at the cost of some extra downlink communication overhead. To strike a trade-off between personalization and communication efficiency, we propose a broadcast protocol that limits the number of personalized streams while retaining the essential advantages of our learning scheme. Through simulation results, our approach is shown to enjoy higher personalization capabilities, faster convergence, and better communication efficiency compared to other competing baseline solutions.