This paper proposes a framework and a value-driven process for new software engineering, named 'Software Engineering for Business and Society: SE4BS', towards the digital transformation (DX) era. Successful DX requires not only technology, but also an understanding of the importance of business agility. In addition, without careful traceability, software engineering projects can be not based on business and social values. To address these issues, we categorize useful methods, practices, and models in software development and operations that make connections and traceability from business ideas incorporating business agility to software products, services, and user experiences. Then we propose a typical value-driven process stemming from business and social perspectives as new software engineering necessary for the DX era. We also categorized these items of the value-driven process through the mental factors of cognition, affective, and conative to analyze the process.