We provide explicit representations for the Dirac structure obtained from an arbitrary number of component Dirac structures coupled by means of another interconnecting Dirac structure. Our work generalizes the results in [1] in two aspects. First, the interconnecting structure is not limited to the simple feedback case considered there, and this opens new possibilities for designing control systems. Second, the number of simultaneously interconnected systems is not limited to two, which allows for extra flexibility in modeling, particularly in the case of electrical networks. Several relevant particular cases are presented, and the application to the interconnection of port- Hamiltonian systems is discussed by means of an example.