Digital Twin is considered a key pillar of the digitalization process. However, the lack of engineering best practices for developing and operating Digital Twins makes the industry difficult to fully benefit from them. Many companies are currently investigating the potential use of Digital Twins, but available solutions are often context-dependent or system-specific, and challenging to adapt, extend, and reuse. Therefore, digital transformation is perceived as a slow, resource-demanding, and extremely expensive process, which outcome is uncertain. To this extent, industries seek solutions allowing them to gently introduce a Digital Twin into their organizations and evolving it according to the changing needs and situations. This paper reports a first attempt on architecting a Digital Twin of the Organization, and discusses some architectural concerns to be addressed in order to facilitate its evolution.