Federated learning (FL) has been considered as a promising learning framework for future machine learning systems due to its privacy preservation and communication efficiency. In beyond-5G/6G systems, it is likely to have multiple FL groups with different learning purposes. This scenario leads to a question: How does a wireless network support multiple FL groups? As an answer, we first propose to use a cell-free massive multiple-input multiple-output (MIMO) network to guarantee the stable operation of multiple FL processes by letting the iterations of these FL processes be executed together within a large-scale coherence time. We then develop a novel scheme that asynchronously executes the iterations of FL processes under multicasting downlink and conventional uplink transmission protocols. Finally, we propose a simple/low-complexity resource allocation algorithm which optimally chooses the power and computation resources to minimize the execution time of each iteration of each FL process.