Healthcare is a primary domain where digital twins are being explored and applied. In this context, the main perspective explored in research and industry insofar is about the virtualization of standalone assets—such as devices, structures, and patients—in a digital twin as-an-application perspective. However, in the real world, these assets are often related to each other, taking part in the same processes and physical ecosystem. In this article, we discuss a vision in which digital twins are used to virtualizing contexts and situations involving multiple related strategic assets of a health organization, resulting in ecosystems of digital twins based on a digital-twin as-a-service perspective. Trauma management is considered as a specific concrete real-world example; nevertheless, open ecosystems of digital twins appear to be a blueprint for virtualizing complex physical realities applicable across different application domains.