The prevailing paradigm describes Sustainable Impact Accelerators (SIA) as supporting organizations that select sustainable new ventures and focus on scaling them. We find that SIAs go beyond selection and actively engage with their portfolio companies in managing the tensions that arise from integrating three logics: sustainable value creation, commercial viability, and rapid scaling. We draw on qualitative and quantitative data from fifteen early-stage new venture cases in an SIA context to build a theory of blended value acceleration. Our theory describes a process that aims to find logic compatibility at selection, improve logic centrality by treatment, and create accountability to avoid the vicious cycles that could derail a sustainable new venture from its mission of blending sustainability and commercial value creation. By providing insights into the SIA’s operation, our theory offers clarity and conceptualization of the impact acceleration process, creating future research pathways on the managerial improvement of sustainable impact accelerator programs.