We propose an integrated framework for adaptive routing in multi-task, multi-modal prediction settings where data heterogeneity and task interactions vary across samples. Inspired by psychotherapy applications where structured assessments and unstructured clinical notes coexist with partially missing data and correlated outcomes, we introduce a routing-based architecture that dynamically selects modality processing paths and task-sharing strategies on a sample-by-sample basis. The model defines multiple modality paths, including raw and fused representations of text and numeric features, and learns to route each input through the most informative combination of experts. Task-specific predictions are generated by shared or independent heads based on routing decisions, and the overall system is trained end-to-end. We evaluate the model using both synthetic data and real psychotherapy notes for depression and anxiety outcome prediction. Experimental results demonstrate that the proposed method consistently outperforms fixed multi-task or single-task baselines, and the learned routing policy provides interpretable insights into modality relevance and task structure. This addresses a critical challenge in personalized medicine by enabling individually adaptive information processing that accounts for data heterogeneity and task correlation. When applied to psychotherapy, this framework can improve mental health outcomes, enhance treatment allocation accuracy, and increase clinical cost-effectiveness through personalized intervention strategies.