Coordination between two or more multiple access channel (MAC) receivers can enlarge the achievable rate region of the whole system. This paper focuses on coordination by sharing the codebooks of the users between the receivers of MACs. We first define the achievable rate region of the time invariant multiple coordinated MAC (MCMAC) and subsequently derive its achievable rate region. We later express the achievable rate region in terms of the dominating points. We base our numerical analysis on the two-user two-receiver Gaussian coordinated MAC and make comparison with the interference channel, full cooperation and the individual MAC performance analysis. It is observed that this approach though suboptimal is less complex in comparison with full cooperation and that the MCMAC rate region is at least equal to the rate region of the uncoordinated approach. Over several channel states, the rate region of MCMAC exceeds that of the uncoordinated approach.