Classifications of higher education institutions into categories that are more or less clearly differentiated through prestige and status are legion in the world of higher education. The notion of parallel categories with comparable statuses, such as those of different types of universities, is however much less well understood. This paper investigates how universities navigate between such alternative categories. We examine boundary work and institutional change involving Swedish higher education institutions with significant activity in engineering sciences in order to analyse how actors relate to ideas regarding the category ‘technical university’ as an ideal potentially distinct from that of the broad, comprehensive university. Analysis of two cases in the second half of the twentieth century shows that for engineering faculty, a focused technical university was an attractive alternative to the institutional model of the broad university. In contrast, analysis of two twenty-first-century cases suggests that aspirations to be recognised as a technical university were largely driven by adaption to external stakeholders’ interests. We discuss these findings in light of the emergence of the global hegemonic category ‘research university’. We also suggest that the organisational identity of a HEI may be tied to ideas about an organisational category through imprinting and path dependency. Moreover, we propose that changes over time in how categories are perceived may serve as an impetus to organisational change.