Well, you couuuuuuuld do it that way, but why would you? Either your consultant has never done a successful process implementation, or he's looking for work to do!
From a process perspective, what is the practical difference between:
IPM and PP?
PP and PMC?
PP/PMC and RSKM
TS and PI?
REQM and RD?
The answer is that these are not silos, but threads, and the expectations (policy) of using the process (and the process itself) should be based around those threads, not around the PAs.
So you might have one policy for the Project Management PAs, another around the Engineering PAs, and so on. The categories in the CMMI continuous representation (Project Mgmt, Process Mgmt, Support, and Engineering) might be a good place to start.