Abstract: Federated multi-task learning (FMTL) has emerged as a promising framework for learning multiple tasks simultaneously with client-aware personalized models. While the majority of studies have focused on dealing with the non-independent and identically distributed (Non-IID) characteristics of client datasets, the issue of task heterogeneity has largely been overlooked. Dealing with task heterogeneity often requires complex models, making it impractical for federated learning in resource-constrained environments. In addition, the varying nature of these heterogeneous tasks introduces inductive biases, leading to interference during aggregation and potentially resulting in biased global models. To address these issues, we propose a hierarchical FMTL framework, referred to as \mathttFedBone , to facilitate the construction of large-scale models with improved generalization. \mathttFedBone leverages server-client split learning and gradient projection to split the entire model into two components: 1) a large-scale general model (referred to as the general model) on the cloud server, and 2) multiple task-specific models (referred to as client models) on edge clients, accommodating devices with limited compute power. To enhance the robustness of the large-scale general model, we incorporate the conflicting gradient projection technique into \mathttFedBone to rectify the skewed gradient direction caused by aggregating gradients from heterogeneous tasks. The proposed \mathttFedBone framework is evaluated on three benchmark datasets and one real ophthalmic dataset. The comprehensive experiments demonstrate that \mathttFedBone efficiently adapts to the heterogeneous local tasks of each client and outperforms existing federated learning algorithms in various dense prediction and classification tasks while utilizing off-the-shelf computational resources on the client side.