A large summerstock festival has a "stable" of 6 stage managers, supplemented by 3-8 contractors and a further 10-15 apprentices and interns. (Depending on the complexity of the season, the precise use of venues, etc.)
Every year, one of the core SMs (usually the job rotates among 3 people in particular) is elevated to serve as PSM, and the job involves what essentially amounts to coordinating the stage management department.
- Scheduling and coordinating use of rehearsal and performance space.
- Representing stage management at progress and planning meetings.
- Updating and drafting health and safety documentation and policies.
- Being on-call 24/7 during the festival itself for any manner of emergency.
- Serving as the primary point of executive contact between the production departments and stage management. ("We'd like to schedule the costume fittings as follows", rather than having each show submit requests independently and making wardrobe sort them out.)
- Hiring and supervising the contractor SMs. (As well as the apprentices, etc.)
- Serving as a keyholder for the festival. (One of only 3 people with an absolute master key, the other two being the General Manager and the head of security.)
- Hiring and coordinating non-production contractors. (Fight directors, accent coaches, etc.)
- A few other duties in this line.
Because of the workload this generates (and especially because of their position at the top of the emergency call list), the PSM cannot take a show of their own. A summer as PSM is a "summer off" from stage management, but it's a job which has to be done, and which is done best by someone who knows the realities of stage management within this festival environment.
Other companies will do things differently. The thing with Summerstock is that it generates a lot of work in a short period of time. In a rep company, the PSM could conceivably balance their executive work with some hands-on stage management: the company produces 12 shows a year, and the PSM--if they're so inclined--might take one or two.