The capacity region for a multiple access channel (MAC) with arbitrary sets of common messages was derived by Han in 1979, extending a result by Slepian and Wolf from 1973. The general characterization by Han involves one auxiliary random variable per message and one inequality per subset of messages. In this paper, at first, a special hierarchy of common messages is identified for which the capacity region is characterized with generally fewer auxiliary random variables and inequalities. It is also shown that this characterization requires no auxiliary random variable for certain message structures. A procedure is then proposed to transform any common message structure to this special hierarchy, leading to a general capacity characterization which generally requires fewer auxiliary random variables than the one given by Han.