Purpose This paper explores how the procurement function initiates and develops relationships with social enterprises that are intended to induce social impact in the supply networks of for-profit firms. Design/methodology/approach The paper utilises an in-depth case study involving a focal company, first-tier supplier, nongovernmental organisation and four social enterprises. Findings Tension mitigation that arises between social and commercial logics occurs via individual relationships through building trust, dependency manipulation, monitoring and supplier development activities. Deeper insights are revealed when triadic relationships are viewed within a quadratic relationship configuration that enables better capturing the essence of supply networks. Research limitations/implications The paper is based on a single case study, limiting empirical generalisability. Future research could consider multiple case studies to reveal different types of relationship configurations that induce social impact in supply networks. Practical implications Societal goals can be met while maintaining supply network economic performance if procurement involves a trusted third party such as a nongovernmental organisation and helps to develop social enterprises as suppliers. Originality/value The paper contributes to the sustainable supply chain management literature by reporting on a novel procurement approach for enhancing social sustainability through cooperation with social enterprises. The paper also contributes to supply network theory by demonstrating how exploring quadratic relationships can reveal novel relationship configurations within supply networks.