Collaborative cross-sector business models for sustainability innovation (CCSBMSI) in response to grand challenges are rich foci for tensions. This is the case of CCSBMSI targeting independent living through Information and Communication Technology–enabled care. This research aims at identifying the relevant tensions, understanding their interactions, and assessing how they can be effectively managed so that CCSBMSI become more valuable for partners and transformative for society. A conceptual framework that understands the management of interrelated institutional and interorganizational tensions as a dynamic capability is substantiated through in-depth, qualitative analysis of the long-term dynamics of a four-sector CCSBMSI in telecare—including government, businesses, nonprofits, and informal actors. Its effects on the transition of business models in terms of value creation, delivery, and capture; on relevant stakeholders—particularly nonprofits and beneficiaries; and on the development of the sustainability innovation are discussed. The conceptualization, tension categories, and management capabilities of CCSBMSI are amplified.