This paper introduces a learning analytics policy and strategy framework developed by a cross-European research project team -- SHEILA (Supporting Higher Education to Integrate Learning Analytics), based on interviews with 78 senior managers from 51 European higher education institutions across 16 countries. The framework was developed adapting the RAPID Outcome Mapping Approach (ROMA), which is designed to develop effective strategies and evidence-based policy in complex environments. This paper presents four case studies to illustrate the development process of the SHEILA framework and how it can be used iteratively to inform strategic planning and policy processes in real world environments, particularly for large-scale implementation in higher education contexts. To this end, the selected cases were analyzed at two stages, each a year apart, to investigate the progression of adoption approaches that were followed to solve existing challenges, and identify new challenges that could be addressed by following the SHEILA framework.