  We show that the classical capacity of quantum states, as quantified by its
ability to perform dense coding, respects an exclusion principle, for arbitrary
pure or mixed three-party states in any dimension. This states that no two
bipartite states which are reduced states of a common tripartite quantum state
can have simultaneous quantum advantage in dense coding. The exclusion
principle is robust against noise. Such principle also holds for arbitrary
number of parties. This exclusion principle is independent of the content and
distribution of entanglement in the multipartite state. We also find a strict
monogamy relation for multi-port classical capacities of multi-party quantum
states in arbitrary dimensions. In the scenario of two senders and a single
receiver, we show that if two of them wish to send classical information to a
single receiver independently, then the corresponding dense coding capacities
satisfy the monogamy relation, similar to the one for quantum correlations.
