Facilitators must work together with stakeholders. The best way to achieve this is to make facilitators integral part of project teams.
However, when multiple teams and multiple facilitators are involved, the work requires coordination. It is important to form an explicit department that builds its own culture and learns from past experiences.
Such a department is not dissimilar to other roles in a software development house. For example, system administrators typically have an own department so that they can coordinate their solutions both from a know-how and from a technology point of view.
The same situation is encountered with assessment facilitators. The work involves both a dedicated skill that can be enhanced through team work, and a technology that has to be mastered.
It is often the case that the same infrastructure is required in multiple projects. In this case, the effort of a tooling buildup phase can be shared and coordinated through the assessment department.
The assessment department is essentially a software team specialized in the domain of analysis. As such, it should function similarly to the rest of the software teams.