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Massive multiple-input multiple-output (mMIMO) communications are one of the enabling technologies of 5G and beyond networks. While prior work indicates that mMIMO networks employing time division duplexing have a significant capacity growth potential, deploying mMIMO in frequency division duplexing (FDD) networks remains problematic. The two main difficulties in FDD networks are the scalability of the downlink reference signals and the overhead associated with the required uplink feedback for channel state information (CSI) acquisition. To address these difficulties, most existing methods utilize assumptions on the radio environment such as channel sparsity or angular reciprocity. In this work, we propose a novel cooperative method for a scalable and low-overhead approach to FDD mMIMO under the so-called grid-of-beams architecture. The key idea behind our scheme lies in the exploitation of the near-common signal propagation paths that are often found across several mobile users located in nearby regions, through a coordination mechanism. In doing so, we leverage the recently specified device-to-device communications capability in 5G networks. Specifically, we design beam selection algorithms capable of striking a balance between CSI acquisition overhead and multi-user interference mitigation. The selection exploits statistical information, through so-called covariance shaping. Simulation results demonstrate the effectiveness of the proposed algorithms, which prove particularly well-suited to rapidly-varying channels with short coherence time.