Employing a Digital Twin of the Organization would help enterprises to change and innovate, thus enhancing their organization’s sustainability. However, the lack of engineering best practices for developing and operating a Digital Twin of the Organization makes it difficult for enterprises to fully benefit from it. Many companies are currently investigating the potential use of it, but available solutions are often context-dependent or system-specific, and challenging to adapt, extend, and reuse. Therefore, digitalization is perceived as a slow, resource-demanding, and extremely expensive process whose outcome is uncertain. To this extent, enterprises seek solutions allowing them to gently introduce a Digital Twin of the Organization into their organization and to evolve it according to the changing needs and situations. This paper reports a first attempt on architecting a Digital Twin of an Organization, and discusses some architectural concerns to be addressed in order to facilitate its development and evolution.