The answer depends on 3 things: The project, the project manager, and the company.
- The project: How big it is? Is it a small project with a few resources working on? Or is it a large construction project? (of course, in the latter case, you can only manage one project. Not only that, there may be more than one project manager on the same project).
- The project manager: How good he is? Is he an experienced project manager or just a rookie? Experienced project manager can manage up to 5 projects at the same time while maintaining the same quality of work, inexperienced project managers can barely manage one project.
- The company: Is there a lot of politics in the company? Are project managers stressed? Is delegating tasks scrutinized by management? Is work fun (this will increase productivity)?
If the project manager is managing a lot of projects, from a higher level, and delegating most of the routine project management tasks to others, then at this point, then he's no longer a project manager, he's a program manager.
Yes, in most cases, managing multiple projects will reduce the project manager's net productivity per project. If the company has many projects being executed, but managed by one project manager, then it would be the wise thing to do to hire more project managers.
Now to answer your question, "how many projects per project manager"? My answer it should never be more than 5.
Again, the number differs by project manager, and you can know what is his limit by seeing how much slack time does the project manager have during his working hours. Once he has no more slack time, then he has reached his limit (which should be no more than 5 projects).