The capacity of the multiple-access channel with any distribution of messages among the transmitting nodes was determined by Han in 1979 and the expression of the capacity region contains a number of rate bounds and that grows exponentially with the number of messages. We derive a more compact expression for the capacity region of this channel in which the number of rate bounds depends on the distribution of the messages at the encoders. Using this expression we prove capacity for a class of general cognitive network that we denote as "very strong interference" regime. In this regime there is no rate loss in having all the receivers decode all the messages and the capacity region reduces to the capacity of the compound multiple-access channel. This result generalizes the "very strong interference" capacity results for the interference channel, the cognitive interference channel, the interference channel with a cognitive relay and many others.