The modernisation of official statistics requires facilitating new forms of data collaboration between National Statistical Offices (NSOs), researchers, government agencies, and the private sector. However, privacy concerns, legal constraints, and organisational risks associated with data access often prevent valuable initiatives from being realised. This paper argues that privacy-enhancing technologies (PETs) can fundamentally transform how sensitive data is accessed and used, enabling these barriers to be more readily overcome, and thus unlocking data collaborations that would otherwise be impossible. Drawing on examples of pilot deployments conducted through the United Nations PET Lab, we demonstrate how applying combinations of PETs can provide robust privacy guarantees and granular governance controls that enable effective use of sensitive data assets. We provide a vision for a new ecosystem for official statistics where NSOs and researchers can securely access thousands more datasets from across sectors and jurisdictions.