Purpose: Continuous Software Engineering (CSE) promises improved efficiency, quality, and responsiveness in software-intensive organizations. However, fully adopting CSE is often constrained by complex products, legacy systems, organizational inertia, and regulatory requirements. In this paper, we examine four industrial cases from the automation, automotive, retail, and chemical sectors to explore how such constraints shape CSE adoption in practice. Methods: We apply and extend a previously proposed CSE Industry Readiness Model to assess the current and potential levels of adoption in each case. Through expert interviews and narrative synthesis, we identify common driving forces and adoption barriers, including organizational preparedness, cross-organizational dependencies, and limited customer demand for continuous delivery. Results: Based on our findings, we propose an updated readiness model that introduces additional levels of internal and external feedback, distinguishes market- and organization-facing constraints, and better guides practitioners in setting realistic CSE adoption goals. Conclusions: Our results highlight that while full end-to-end CSE adoption may not always be feasible, meaningful internal improvements are still possible and beneficial. This study provides empirically grounded guidance for organizations navigating partial or constrained CSE transformations.