A recent work by Kapidani and Vázquez, J. Comp. Phys. (2023), presented a new isogeometric method for the solution of electromagnetic wave problems in a first order formulation. The method is based on the construction of a dual sequence by a simple degree change, without introducing a dual grid, and the definition of discrete Hodge-* operators, which encapsulate the material properties, to pass information between the two sequences. The method conserves exactly energy and charges, it attains high order of convergence, it is free of spurious modes, and can be solved very efficiently due to the tensor-product structure of the pairing matrices appearing in the Hodge-* operators. Its drawback is that it is limited to single-patch geometries. In this work we extend the method to general multi-patch geometries. The continuous problem is formulated within a discontinuous Galerkin framework, following the formulation previously used for Friedrichs' systems, and boundary conditions are imposed weakly. However, with this choice the pairing matrices appearing in the Hodge-* operators become rectangular. To recover square matrices with tensor-product structure, we modify the spaces of the dual de Rham sequence. Similarly to Nédélec's finite elements of the second family, this choice introduces spurious modes, but it retains conservation of energy, high order of convergence and computational efficiency. Numerical experiments indicate that the performance of the proposed method is comparable to that of the original solver, while its applicability is extended to a large familiy of domains.