Health care is a complex domain containing large amounts of data, including clinical and administrative data. Furthermore, the domain includes advanced decision-making utilising the collected data. Various IT systems based on AI technologies, such as machine learning, have been promoted as a way to improve both the quality and efficiency of health care. So far, the focus has been on supporting quite narrow and data-intensive activities carried out by a single actor, such as interpreting X-ray images and performing triage. However, providing health care for a single patient can involve a comprehensive process with numerous actors, ranging from home care and primary care to specialist care. In this paper, we examine how existing AI solutions can support a complex care process involving several collaborating actors. We base the examination on a health care case from Swedish elderly care. The case is used to identify multiple problem areas, which are then compared to existing AI solutions