Great answers from everybody.
I want to append on @Perry Wilson's answer regarding "strengthening the methodology and standardizing process", i.e. which Project Models you use within your company.
In the company I worked for (as Process Leader of Product Portfolfio Development process), we had bought a lot of companies and all had their own Project Models. In all the procured companies their own Project Models were deeply "in the walls".
Since coworkers, especially from Customer Support organization, were involved in more than one project and often in projects with different Project Models for the same type of project, there were a lot of time/cost lost due to "different language".
Therefore we started a huge project to merge them all together. It was not only to get the phase definitions/scope standardized, but also the nomenclature. We had so many synonyms used and also mixed.
With that cleaned up and defined, we finally printed booklet and sent it out to everybody working in projects, at any level.
For this to work, we made the booklet light weight, meaning the most important information per phase on two adjacent pages. This made it easy for readers to read through quickly, and they could also have the current phase of projects they worked in open, standing on their desk. (Beside the booklet, we also had a more extensive version of the Project Model online, as well as forms for asking questions, notify of misprints or even post change proposals.)
The CEO ordered everybody to read them and then we followed it up with further training for everybody that had got a booklet - more or less the whole organization (and this is a big company).
This had a huge impact.
- We had a standardized Project Model regarding phases, steps, deliverables, milestones, requirements to pass gates.
- We used same templates and systems for documentation.
- We spoke the same "language" - using same terminology.
All this enabled
- Everybody, from Steering Committee members to coworkers, knew their role much better.
- Everybody knew what the different organizational departments (incl. PMO) were responsible of and when responsibility shifted (for example from a PreStudy to an actual Project, Advanced Engineering, from Project to PreMarket...).
- It was easier to support another coworker and have back ups.
- And perhaps the most relevant for this question - it sure strengthened the knowledge and support of the PMO.
Fun Fact - The name of the Project Model is now even used in job ads by consultant companies when they are looking for people to work in this company.