Digital twins have gained tremendous momentum since their conceptualization over 20 years ago, as more and more domains discover their value in driving efficiencies and reducing costs, while enabling technologies continue to advance. Originally aimed at product optimization and intelligent manufacturing, the range of applications for digital twins now spans entire complex, often highly interconnected systems such as ports, cities, and supply chains. Despite the increasing demand for sophisticated digital twinning solutions across all domains and scopes, their development is often still constrained by differing definitions, different understandings of their functional scope and design, and a lack of concrete methodology toward implementing a comprehensive digital twinning solution. Although there are already papers that evaluate the capabilities of existing digital twinning solutions on the basis of maturity levels, these usually consider the object to be twinned in isolation and are often domain-specific. With this article we address exactly this gap discussing how interoperability of digital twins can break physical boundaries of an isolated system, enabling system of systems joint optimization. We therefore consider interoperable digital twins to be the most mature twinning platforms, thus, we discuss in detail six digital twin maturity levels, departing from the interrelated contexts of ports, cities, and supply chains. Examples drawn from these domains demonstrate the need for interoperability toward optimizing processes and systems in realistic contexts, rather than in assumed isolation.