Traditional learning-based approaches to student modeling (e.g., predicting grades based on measured activities) generalize poorly to underrepresented/minority student groups due to biases in data availability. In this paper, we propose a Multi-Layer Personalized Federated Learning (MLPFL) methodology which optimizes inference accuracy over different layers of student grouping criteria, such as by course and by demographic subgroups within each course. In our approach, personalized models for individual student subgroups are derived from a global model, which is trained in a distributed fashion via meta-gradient updates that account for subgroup heterogeneity while preserving modeling commonalities that exist across the full dataset. To evaluate our methodology, we consider case studies of two popular downstream student modeling tasks, knowledge tracing and outcome prediction, which leverage multiple modalities of student behavior (e.g., visits to lecture videos and participation on forums) in model training. Experiments on three real-world datasets from online courses demonstrate that our approach obtains substantial improvements over existing student modeling baselines in terms of increasing the average and decreasing the variance of prediction quality across different student subgroups. Visual analysis of the resulting students' knowledge state embeddings confirm that our personalization methodology extracts activity patterns which cluster into different student subgroups, consistent with the performance enhancements we obtain over the baselines.