Background: Capturing complete medical knowledge is challenging-often due to incomplete patient Electronic Health Records (EHR), but also because of valuable, tacit medical knowledge hidden away in physicians' experiences. To extend the coverage of incomplete medical knowledge-based systems beyond their deductive closure, and thus enhance their decision-support capabilities, we argue that innovative, multi-strategy reasoning approaches should be applied. In particular, plausible reasoning mechanisms apply patterns from human thought processes, such as generalization, similarity and interpolation, based on attributional, hierarchical, and relational knowledge. Plausible reasoning mechanisms include inductive reasoning, which generalizes the commonalities among the data to induce new rules, and analogical reasoning, which is guided by data similarities to infer new facts. By further leveraging rich, biomedical Semantic Web ontologies to represent medical knowledge, both known and tentative, we increase the accuracy and expressivity of plausible reasoning, and cope with issues such as data heterogeneity, inconsistency and interoperability. In this paper, we present a Semantic Web-based, multi-strategy reasoning approach, which integrates deductive and plausible reasoning and exploits Semantic Web technology to solve complex clinical decision support queries. Results: We evaluated our system using a real-world medical dataset of patients with hepatitis, from which we randomly removed different percentages of data (5%, 10%, 15%, and 20%) to reflect scenarios with increasing amounts of incomplete medical knowledge. To increase the reliability of the results, we generated 5 independent datasets for each percentage of missing values, which resulted in 20 experimental datasets (in addition to the original dataset). The results show that plausibly inferred knowledge extends the coverage of the knowledge base by, on average, 2%, 7%, 12%, and 16% for datasets with, respectively, 5%, 10%, 15%, and 20% of missing values. This expansion in the KB coverage allowed solving complex disease diagnostic queries that were previously unresolvable, without losing the correctness of the answers. However, compared to deductive reasoning, data-intensive plausible reasoning mechanisms yield a significant performance overhead.