Shaping social competences of university graduates constitutes one of the most important contemporary challenges. The cognitive objectives of the Erasmus + DASCHE project, the selected results of which are presented in this article, were (1) to identify good practices in shaping social competences of students in selected higher education institutions, (2) to support public policies with regard to higher education at both European and national levels, as well as at higher education institutions (HEIs) in the area of designing, shaping and verifying students’ social competences and formulating recommendations in this regard. For these purposes, case studies at 26 selected HEIs were carried out within the project. This article presents an analysis of public policies in Germany, the Netherlands, Poland, Latvia, the Czech Republic and the United Kingdom in the context of influence of these policies on whether and how HEIs shape students’ social competences and whether HEIs are obliged, encouraged or supported by legal regulations and other instruments in this regard. The research shows a large diversity of national public policies in this respect and - with the widespread recognition by the academic staff of the importance of shaping student attitudes - a significant lack of intentional actions leading to shaping students’ competences at the national, institutional and European level.