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We prove coding theorems for two scenarios of cooperating encoders for themultiple access channel with two classical inputs and one quantum output. Inthe first scenario (ccq-MAC with common messages), the two senders each havetheir private messages, but would also like to transmit common messages. In thesecond scenario (ccq-MAC with conferencing encoders), each sender has its ownset of messages, but they are allowed to use a limited amount of noiselessclassical communication amongst each other prior to encoding their messages.This conferencing protocol may depend on each individual message they intend tosend. The two scenarios are related to each other not only in spirit - theexistence of near-optimal codes for the ccq-MAC with common messages is usedfor proving the existence of near-optimal codes for the ccq-MAC withconferencing encoders.

The Classical-Quantum Multiple Access Channel with Conferencing Encoders and with Common Messages