Many studies in traditional business model (BM) literature acknowledge that it is hard for incumbent firms to change their business models, a finding echoed in the business model innovation for sustainability (BMIfS) literature. Large incumbent firms often lack or have weak capabilities needed for sustainability-driven business model innovation. This paper addresses how capabilities for such innovation evolve in large incumbent firms. The research builds on a longitudinal case study in the energy utility industry, and on two theoretical frameworks advanced in previous literature: values-based business model innovation, and capability lifecycles. We conceptually propose a stage-based maturity model of BMIfS. Our model highlights three types of research contributions. First, we propose that the capability development underpinning BMIfS is a nonlinear process of distinct maturity stages. Second, the maturity stages have intermediate transformation junctures that the firm must go through. These junctures either change or initiate the conditions for capability development to be able to advance to the next BMIfS maturity level. Third, the shift in societal, regulatory, competitor, and customer expectations and interests triggers strategic decisions and early development of capabilities that start and push the firm into the transformation junctures.