While transfer learning is an effective strategy, it often overlooks the opportunity to leverage knowledge from numerous available models online. Addressing this multi-source transfer learning problem is a promising path to boost adaptability and cut re-training costs. However, existing methods remain inherently coarse-grained: they lack the precision needed for fine-grained knowledge extraction as well as the scalability required to aggregate knowledge from either large numbers of source models or models with high parameter counts. We address these limitations by leveraging Singular Value Decomposition (SVD) to first decompose each source model into its elementary, rank-one components. A subsequent aggregation stage then selects only the most salient components from all sources, thereby overcoming the previous efficiency and precision limitations. To best preserve and leverage the synthesized knowledge base, our method adapts to the target task by fine-tuning only the principal singular values of the merged matrix. In essence, this process recalibrates the importance of top SVD components. The proposed framework allows for efficient and scalable multi-source transfer learning in both vision and language domains, while remaining robust to perturbations in both the input space and the parameter space.