Boards in higher education organizations (HEOs) play multiple roles. While they govern, boards are also expected to embed HEOs in society. Indeed, recent higher education reforms in Europe have emphasized the embedding role of HEO boards more than their governing role. But, although these reforms are widespread, we still know little about the ways in which boards are affected by ambitions of embedding HEOs. The aim of our paper is to explore how such ambitions are expressed through HEO board nominations and compositions. We address this aim by turning to Sweden, whose higher education system has, during the past three decades, undergone recurrent reforms that emphasize the embedding role of boards at public HEOs. Our study builds on a longitudinal dataset of external HEO board members' positions, employers, and simultaneous board seats, collected for 1998, 2007, and 2016 so as to accompany Swedish reforms. We find that external board members, over time, embedded HEOs in expanding and sprawling networks of ties to organizations from the public, private, and civil society sectors. Our findings push the literature beyond its focus on private sector ties by showing how governmental reforms lead HEOs to embed among public and civil society organizations as well.