Universities play an important role in the development of society. However, it is not always clear what the objectives of collaboration between a Higher Education Institution (HEI) and external stakeholders from the surrounding society are. In this study, value-focused thinking was applied to construct structures of strategic, fundamental and means objectives of different stakeholders working practically with collaboration between an HEI and the surrounding society. Respondents in three groups of stakeholders from a university and external parties were interviewed. Focus in this study is on general objectives of collaboration between an HEI and the surrounding society. Based on the interviews and feedback, objectives were identified and SSFMO (Structure of Strategic, Fundamental and Means Objectives) was constructed from each respondent's answer. Generally, the fundamental objectives differed more between the stakeholders than the means objectives did. How SSFMOs could be used in practical collaboration projects is discussed in the paper.