With its privacy preservation and communication efficiency, federated learning (FL) has emerged as a learning framework that suits beyond 5G and towards 6G systems. This work looks into a future scenario in which there are multiple groups with different learning purposes and participating in different FL processes. We give energy-efficient solutions to demonstrate that this scenario can be realistic. First, to ensure a stable operation of multiple FL processes over wireless channels, we propose to use a massive multiple-input multiple-output network to support the local and global FL training updates, and let the iterations of these FL processes be executed within the same large-scale coherence time. Then, we develop asynchronous and synchronous transmission protocols where these iterations are asynchronously and synchronously executed, respectively, using the downlink unicasting and conventional uplink transmission schemes. Zero-forcing processing is utilized for both uplink and downlink transmissions. Finally, we propose an algorithm that optimally allocates power and computation resources to save energy at both base station and user sides, while guaranteeing a given maximum execution time threshold of each FL iteration. Compared to the baseline schemes, the proposed algorithm significantly reduces the energy consumption, especially when the number of base station antennas is large.