Quantum communication technologies are expected to enable secure communication, distributed quantum computing, and large-scale quantum sensing. Many quantum protocols rely on classical information exchanged between network nodes, as in quantum repeaters and entanglement distribution, where classical messages determine subsequent operations. As quantum technologies continue to integrate with existing infrastructures, understanding the role of classical communication resources in quantum networks becomes increasingly important. A key classical communication resource is feedback: in classical multi-user settings, it can improve achievable rates by enabling cooperation between transmitters. In this work, we study the role of classical feedback in quantum multi-user communication. While the no-cloning theorem prohibits universal copying of arbitrary quantum states, feedback can be generated by measuring the channel outputs and communicating the resulting classical outcomes back to the transmitters. For quantum multiple-access channels, we derive an achievable rate region based on partial-information decoding at the transmitters. We further show that classical feedback strictly enlarges the achievable rate region of the qubit SWAP channel, which captures an optical communication scenario where quantum signals from different sources may be confused at the receiver. These results demonstrate that feedback can enhance communication rates in quantum networks