Comment: 90 pages, 8 figures, 7 tablesModularity is critical for the emergence and evolution of complex social, natural, and technological systems robust to exploratory failure. We consider this in the context of emerging business organizations, which can be understood as complex systems. We build a theory of organizational emergence as higher-order, modular recombination wherein successful start-ups assemble novel combinations of successful modular components, rather than engage in the lower-order combination of disparate, singular components. Lower-order combinations are critical for long-term socio-economic transformation, but manifest diffuse benefits requiring support as public goods. Higher-order combinations facilitate rapid experimentation and attract private funding. We evaluate this with U.S. venture-funded start-ups over 45 years using company descriptions. We build a dynamic semantic space with word embedding models constructed from evolving business discourse, which allow us to measure the modularity of and distance between new venture components. Using event history models, we demonstrate how ventures more likely achieve successful IPOs and high-priced acquisitions when they combine diverse modules of clustered components. We demonstrate how higher-order combination enables venture success by accelerating firm development and diversifying investment, and we reflect on its implications for social innovation.