The digital era and mounting sustainability pressures have reinforced incumbents’ need to respond to radical innovation through business model innovation. Despite advancements in the literature on incumbent business model innovation, there are still open debates regarding strategies for achieving systematic innovation and poor integration between the literature on managing multiple business models and the strategic management of business model innovation. To address these gaps, we investigated three Brazilian incumbents that developed systematic business model innovation processes and analyzed their evolution. We followed a multiple case study methodology, deploying system dynamics as an analytical lens. Our findings showed that the evolution of innovation departments from business model renewal to exploration is based on a systemic tension between solving the core problems of the business and creating openness to innovation, innovation capabilities, and resources. By assigning the innovation departments a vital role in the renewed business model and exploring synergies to manage multiple business models, the companies create a “buffer” to sustain exploratory business model innovation. We suggest that the strategy for conducting business model renewal matters, especially when the renewal is transformative, aiming to shape the future. We contribute to incumbent business model innovation theory by showing the system dynamics behind the evolution from business model renewal to exploration and by connecting the management of parallel business models to the strategic management of business model innovation.