The current world of higher education (HE) has been shaped by two forces: the humanistic traditions of university governance and the neo-liberal reforms of the past thirty years. With its successes and discontents, this hybrid system faces major crises that affect its ability to respond to the needs of society: the tension between traditional and neo-liberal academic values; the biased evaluation and assessment of quality in higher education; the ineffectiveness determined by the distorted measurements of scientific achievements and other factors; the recent digital transformations of the universities facing the pandemic. To face these challenges, HESPRI addresses innovative strategies to strengthen public policies and improve the competitiveness of the HE sector. Specific objectives and originalities, and a well-designed R&I work plan (4 scientific WPs and 2 support WPs) are proposed for achieving this main goal: comparing a range of national HE systems worldwide as a function of cultural practices, for revealing tensions between various categories of values, shaped by global tendencies; exploring, defining and comparing quality in HE in different contexts, in order to provide innovative and advanced methodology; bringing the collective voice of science into the policymaking process in HE, by looking at how disciplinary and national differences affect governance; analysing technology-enhanced higher education environments, beyond the state of the art, around three pillars - digitalisation, metaverse and open science, on specific emerging research topics. Relying on a world-class and culturally diverse consortium, HESPRI aims to provide evidence-based recommendations for governments, policymakers and universities, to adjust various components in trend with recent provocations. The project proposal incorporates global digitalisation trends, and is tightly connected with world-wide and European strategies and programmes, such as the UN global policies of SDGs.