This paper explores the innovative dynamics established through the European Universities Initiative (EUI) and their role in steering collaborative, challenge-driven research with societal impact. The EUI fosters the creation of university alliances aimed at aligning education and research with societal needs within the European Research Area. These alliances are designed to enhance transnational cooperation, particularly via developing common science agendas that serve as joint research strategies designed to deepen scientific collaboration among alliance partners. These agendas are structured around key priorities such as sustainability, inter- and transdisciplinary research, and adherence to Responsible Research and Innovation principles. Our study focuses on the CHARM-EU Alliance as a case study, presenting a participatory process for building multidisciplinary academic teams to define scientific priorities aligned with sustainable development goals. The process provides a practical tool for fostering new scientific networks to identify and tackle complex global issues, being replicable, inclusive, and adaptable for other alliances. Additionally, the paper discusses the main barriers encountered in developing and implementing a procedure to set up a common science agenda, including the challenges of inter-institutional collaboration and the integration of diverse institutional policies and priorities. Our findings offer insight into the successes and limitations of such initiatives, contributing to a collective learning experience that can inform policy and academic communities on fostering transformative research strategies within university alliances.