The rapid proliferation of domain-specialized machine learning models presents a challenge: while individual models excel in specific domains, their performance varies significantly across diverse applications. This makes selecting the optimal model for new tasks,especially with limited or no domain-specific data, a difficult problem. We address this challenge by formulating it as a multiple-source domain adaptation (MSA) problem. We introduce a novel, scalable algorithm that effectively routes each input to the best-suited model from a pool of available models. Our approach provides a key performance guarantee: for any new domain that lies within the convex hull of the source domains, the accuracy achieved by the best source model is maintained. This guarantee is formally established through a theoretical bound on the regret for new domains, expressed as a convex combination of the best regrets in the source domains, plus a concentration term that diminishes as the amount of source data increases.