Most schemes that rank universities for their level of internationalisation are based on compositional criteria, such as the numbers of international students and staff, and student mobility numbers. Yet if such diversity is to be meaningful beyond financial benefits and enhance the quality of education and research, including stimulating growth in (inter alia) intercultural competence, other measures are needed. Research in the intercultural field indicates that two foundational elements are required for this stimulation: (a) positive attitudes (e.g. openness and curiosity) towards diversity and motivation to learn about/engage with it and (b) experiences of difference that challenge people's viewpoints, ideas and ways of doing things. Yet these variables are rarely probed simultaneously in higher education research. This article reports a study that used a tool to probe both of these elements in combination, in relation to three facets relevant to internationalisation: social integration, academic integration and global opportunities and support. The study draws on data from 2360 students, gathered from four different countries, to explore how the opportunity benefits offered by diversity are being perceived and exploited by the respondents. The interconnections between the variables are explored, along with similarities and differences in ratings across regional groups. The article ends by discussing the conceptual and strategic planning implications of the findings.