The Aparecida bishops make a case for a comprehensive campus ministry:
343. There must be a university ministry accompanying the life and journey of all members of the university community, promoting personal and committed encounter with Jesus Christ and multiple solidarity and missionary initiatives. It must also pursue close relations and dialogue with members of other public universities and research centers.
Not just students. And not just the institution, but relationships with other ministries in sister institutions.
For deeper examination, an English translation of the 2007 document from the Aparecida Conference.