Machine learning algorithms have been used to determine probabilistic classifications of unassociated sources. Often classification into two large classes, such as Galactic and extra-galactic, is considered. However, there are many more physical classes of sources. For example, there are 23 classes in the latest Fermi-LAT 4FGL-DR3 catalog. In this note we subdivide one of the large classes into two subclasses in view of a more general multi-class classification of gamma-ray sources. Each of the three large classes still encompasses several of the physical classes. We compare the performance of classifications into two and three classes. We calculate the receiver operating characteristic curves for two-class classification, where in case of three classes we sum the probabilities of the sub-classes in order to obtain the class probabilities for the two large classes. We also compare precision, recall, and reliability diagrams in the two- and three-class cases.