Machine learning (ML) has increasingly been applied to gamma-ray spectroscopy and isotope identification. Traditionally, the identification of isotopes in a spectrogram relies on domain experts, who use their experience to discern the underlying isotopes. However, such expertise might require a steep learning curve, making fast and automated pipelines for isotope identification highly valuable. This work builds upon existing literature and demonstrates the ability to classify multiple radioisotopes by utilizing a convolutional neural network (CNN). The novelty of this study is that the CNN is trained only on single- and double-isotope gamma-spectrum templates provided by the GAmma Detector Response and Analysis Software—Detector Response Function (GADRAS-DRF) software, but the CNN’s predictions are generalized up to seven different isotopes in a mixture. In addition, preliminary results of the application of a least-squares method to estimate the activity of the identified isotopes are presented. The CNN-based architecture achieved good performance, achieving an F1-score above 0.8 for the majority of isotopes in a mixture containing up to five different isotopes. It also showed potential in handling more complex cases involving mixtures with up to seven isotopes, although with a noticeable decrease in F1-score. Performance reduces as the number of isotopes in the mixture increases. Lowest results are observed in identifying isotopes such as 238U, 239Pu, and 241Am due to the intrinsic properties of these isotopes. This study significantly extends the scope of current literature, demonstrating the potential of ML for more complex isotope identification tasks and by proposing a scalable approach showing that CNNs can effectively classify multiple isotopes in spectrograms, even with a relatively small training dataset, that are based on single-isotope or double-isotope templates.