Data-driven deep learning based code designs, including low-complexity neural decoders for existing codes, or end-to-end trainable auto-encoders have exhibited impressive results, particularly in scenarios for which we do not have high-performing structured code designs. However, the vast majority of existing data-driven solutions for channel coding focus on a point-to-point scenario. In this work, we consider a multiple access channel (MAC) with feedback and try to understand whether deep learning-based designs are capable of enabling coordination and cooperation among the encoders as well as allowing error correction. Simulation results show that the proposed multi-access block attention feedback (MBAF) code improves the upper bound of the achievable rate of MAC without feedback in finite block length regime.