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Machine learning (ML) starts to be widely used to enhance the performance of multi-user multiple-input multiple-output (MU-MIMO) receivers. However, it is still unclear if such methods are truly competitive with respect to conventional methods in realistic scenarios and under practical constraints. In addition to enabling accurate signal reconstruction on realistic channel models, MU-MIMO receive algorithms must allow for easy adaptation to a varying number of users without the need for retraining. In contrast to existing work, we propose an ML-enhanced MU-MIMO receiver that builds on top of a conventional linear minimum mean squared error (LMMSE) architecture. It preserves the interpretability and scalability of the LMMSE receiver, while improving its accuracy in two ways. First, convolutional neural networks (CNNs) are used to compute an approximation of the second-order statistics of the channel estimation error which are required for accurate equalization. Second, a CNN-based demapper jointly processes a large number of orthogonal frequency-division multiplexing (OFDM) symbols and subcarriers, which allows it to compute better log likelihood ratios (LLRs) by compensating for channel aging. The resulting architecture can be used in the up- and downlink and is trained in an end-to-end manner, removing the need for hard-to-get perfect channel state information (CSI) during the training phase. Simulation results demonstrate consistent performance improvements over the baseline which are especially pronounced in high mobility scenarios.