We develop a systematic approach to measuring combinatorial innovation in the biomedical sciences based upon the comprehensive ontology of Medical Subject Headings (MeSH). This approach leverages an expert-defined knowledge ontology that features both breadth (27,875 MeSH analyzed across 25 million articles indexed by PubMed from 1902 onwards) and depth (we differentiate between Major and Minor MeSH terms to identify differences in the knowledge network representation constructed from primary research topics only). With this level of uniform resolution we differentiate between three different modes of innovation contributing to the combinatorial knowledge network: (i) conceptual innovation associated with the emergence of new concepts and entities (measured as the entry of new MeSH); and (ii) recombinant innovation, associated with the emergence of new combinations, which itself consists of two types: peripheral (i.e., combinations involving new knowledge) and core (combinations comprised of pre-existing knowledge only). Another relevant question we seek to address is whether examining triplet and quartet combinations, in addition to the more traditional dyadic or pairwise combinations, provide evidence of any new phenomena associated with higher-order combinations. Analysis of the size, growth, and coverage of combinatorial innovation yield results that are largely independent of the combination order, thereby suggesting that the common dyadic approach is sufficient to capture essential phenomena. Our main results are twofold: (a) despite the persistent addition of new MeSH terms, the network is densifying over time meaning that scholars are increasingly exploring and realizing the vast space of all knowledge combinations; and (b) conceptual innovation is increasingly concentrated within single research articles, a harbinger of the recent paradigm shift towards convergence science.