Higher education's focus is shifting to include societal impact alongside academic excellence. While community-engaged scholarship has a long history, many initiatives focus on individual researchers or institutional practices, without accounting for disciplinary and geopolitical contexts. The Community Engagement for Impact (CEFI) Framework and the Contextual Model of Community Engagement (CMCE) are based on findings of an in-depth, qualitative study of researchers' strategies for community engagement. Results point to complex relationships between researchers, universities, and disciplines, shaped by government policy, research trends, community imperatives, and other factors. While participants fostered community relationships supporting social change, they did not receive appropriate training, support, or recognition. CEFI guides individuals and institutions to identify barriers and facilitators for engagement, across disciplines, for work involving industry organisations, community groups, governments, and other partners. When used alongside CMCE's approach to local, national, and global factors, researchers, universities, and disciplines can better support pathways to societal impact.