Digital twins, which are increasingly adopted in industry, are model-centric systems used to improve the behavior of a twinned physical system. Seen as a whole, this system has several layers of self-adaptation: first, the digital twin manages its physical counterpart and maintains its models through a feedback loop to, e.g., fine-tune model parameters. Second, the digital twin needs to deal with unforeseen changes in the physical system, which require models to be partly replaced or recomposed. We refer to these layers as behavioral and structural self-adaptation, respectively. To facilitate research on self-adaptive digital twins, without requiring access to industrial production systems, this paper presents GreenhouseDT, an exemplar that clearly separates these layers of self-adaptation. GreenhouseDT provides an extensible software architecture for a digital twin of a simple, low-cost greenhouse, in which plants, sensors and water pumps constitute the physical system. A characterizing feature of GreenhouseDT is the inclusion of an asset model in the digital twin’s knowledge base and the use of reflection to lift configurations of simulation models into the knowledge base. We discuss how GreenhouseDT can be extended with different digital twin capabilities, demonstrated by the addition of plant health monitoring and model-based control.