针对多任务多模态联邦学习中的个性化难题，提出两阶段自适应优化方法。

In federated learning (FL), local personalization of models has received significant attention, yet personalized fine-tuning of foundation models remains underexplored. In particular, there is a lack of understanding in the literature on how to personalize foundation models in settings where there exist heterogeneity not only in data, but also in tasks and modalities across the clients. To address this gap, we propose Two-Stage Adaptive Personalization (TAP). In the first stage, TAP leverages mismatched model architectures between clients and the server to selectively replace personalized parameters with global updates, explicitly limiting cross-task and cross-modality interference. In the second stage, TAP conducts post-FL distillation on the global model to recover a beneficial shared structure. By reintroducing generalizable knowledge only after the global model has stabilized, TAP enhances generalization without compromising personalization. In developing our methodology, we introduce the first convergence analysis of federated foundation model training at the server under modality-task pair heterogeneity across clients, and demonstrate the impact of the number of modality-task pairs on model fine-tuning. Through extensive experiments, we demonstrate the effectiveness of TAP across a variety of datasets and tasks in comparison to state-of-the-art baselines. The implementation code is publicly available at https://github.com/lee3296/TAP.