Designing AI systems that capture human-like behavior has attracted growing attention in applications where humans may want to learn from, or need to collaborate with, these AI systems. Many existing works in designing human-like AI have taken a supervised learning approach that learns from data of human behavior, with the goal of creating models that can accurately predict human behavior. While this approach has shown success in capturing human behavior, it also suffers from the drawback of mimicking human mistakes. Moreover, existing models only capture a snapshot of human behavior, leaving the question of how to improve them largely unanswered. Using chess as an experimental domain, we investigate the question of teaching an existing human-like model to be stronger using a data-efficient curriculum, while maintaining the model's human similarity. To achieve this goal, we extend the concept of curriculum learning to settings with multiple labeling strategies, allowing us to vary both the curriculum (dataset) and the teacher (labeling strategy). We find that the choice of teacher has a strong impact on both playing strength and human similarity; for example, a teacher that is too strong can be less effective at improving playing strength and degrade human similarity more rapidly. We also find that the choice of curriculum can impact these metrics, but to a smaller extent. Finally, we show that our strengthened models achieve human similarity at higher-level datasets, suggesting human-like improvement.