It has been suggested that higher education institutions (HEIs) may develop different activity profiles (including research, teaching and socio-economic engagement) in their attempt to maximise the fit between institutional resources and strategic opportunities; the latter include strategies of engagement with different groups of external stakeholders. Understanding the extent to which HEIs' resources and activity profiles are aligned with their strategic prioritisation of stakeholder groups allows us to better understand the different ways in which HEIs drive socio-economic development. Using non-parametric techniques -- qualitative and quantitative ordinal multidimensional scaling -- applied to data on the universe of HEIs in the United Kingdom, we show that HEIs with different institutional resources and undertaking different sets of activities prioritise their engagement with different stakeholder groups. We also confirm the complex associations between HEIs' institutional resources, activity profiles and stakeholder prioritisation strategies, which lock HEIs into configurations that are difficult to change.