As industrial sustainability concerns mount, manufacturers engaged in digital servitization grapple with the twin transition of configuring and implementing digital solutions to meet their customers' sustainability objectives. To address this challenge, a socio-technical systems theory-based framework is proposed. Drawing on case studies with three manufacturers undertaking digital servitization and on the sustainability, digital servitization, and socio-technical systems theory research, our framework highlights key processes in navigating the twin transition. It emphasizes the importance of contextual factors in defining a customer twin-transition roadmap, outlines key steps in reconfiguring technical and social subsystems, and stresses the joint optimization processes based on feedback and metrics. This systematic approach guides manufacturers in supporting their customers through the twin transition, emphasizing socio-technical systems and iterative processes for sustained success. Our findings contribute to the growing digital servitization and sustainability research by conceptualizing underlying processes in the twin transition and offering manufacturers practical insights.