Co-design is a widely applied design process with well-documented values, including mutual learning and collective creativity. However, the real-world challenges of conducting multidisciplinary co-design research to inform the design of self-care technologies are not well established. We provide a qualitative account of a multidisciplinary project that aimed to co-design machine learning applications for Type 1 Diabetes (T1D) self-management. Through retrospective interviews, we identify not only perceived social, technological and strategic benefits of co-design but also organisational, translational and pragmatic design challenges: participants with T1D experienced difficulties in co-designing systems that met their individual self-care needs as part of group design activities; HCI and AI researchers described challenges collaborating to apply co-design outcomes to data-driven ML work; and industry collaborators highlighted academic data sharing regulations as cross-organisational challenges that can impede co-design efforts. Based on this understanding, we discuss opportunities for supporting multidisciplinary collaborations and aligning individual health needs with collaborative co-design activities.CCS Concepts: • Human-centered computing → Collaborative and social computing; Empirical studies in collaborative and social computing;