Additive manufacturing using Powder Bed Fusion by Laser Beam (PBF-LB) enables products with high design freedom. In addition, the ability to process more than one material in all three spatial directions makes it possible to produce highly functional components in one single process. This article investigates whether multi-material manufacturing using PBF-LB is suitable for producing coils for electric motors, which are designed with integrated cooling channels to increase the power density. For this purpose, the copper alloy CuCr1Zr for the coils and the stainless steel 1.4404 (316L) for the core are processed simultaneously. The component designs were verified using 2D and 3D finite element analysis and then manufactured in a multi-material PBF-LB process. While good electrical conductivity of the copper alloy was achieved by heat treatment, it was found that thermal distortion caused deviations from the nominal geometry. The measurement of the electrical properties showed that this distortion leads to short-circuit currents within the coils and the teeth. On this basis, ideas for solutions were developed, with the help of which the functionality of the coils can be ensured or the power density can also be increased. In addition to adapting the design of the component, this includes processing additional or other materials, such as soft magnetic composites.