Future AI systems may need to provide medical professionals with explanations of AI predictions and decisions. While current XAI methods match these requirements in principle, they are too inflexible and not sufficiently geared toward clinicians' needs to fulfill this role. This paper offers a conceptual roadmap for how XAI may be integrated into future medical practice. We identify three desiderata of increasing difficulty: First, explanations need to be provided in a context- and user-dependent manner. Second, explanations need to be created through a genuine dialogue between AI and human users. Third, AI systems need genuine social capabilities. We use an imaginary stroke treatment scenario as a foundation for our roadmap to explore how the three challenges emerge at different stages of clinical practice. We provide definitions of key concepts such as genuine dialogue and social capability, we discuss why these capabilities are desirable, and we identify major roadblocks. Our goal is to help practitioners and researchers in developing future XAI that is capable of operating as a participant in complex medical environments. We employ an interdisciplinary methodology that integrates medical XAI, medical practice, and philosophy.