What quantity and size of projects do you expect a Project Manager to oversee at one time?

PMs and other roles that require time to plan, time to research, time to coordinate, etc. could be booked as much as 75% of their day, so about 6 hours. How each PM reaches that maximum booking time depends on the distinct project requirements, A PM managing 12 projects that require no more than 30 minutes each per day could make the metric work. However, a PM engaged in an organization transforming project might only be able to PM that one project. Beyond a simple benchmark like this, the real answer depends on the skill and experience of the specific PM. 

It depends on the project manager, their skills and experience and the size of the project.  I have had very senior PM's manage a single "project" and junior PM's handle multiple small projects at once.  

This is not a question with an answer other than "it depends".  

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My expectations for a PM are mostly determined by the level of difficulty and scope of the projects that are currently being worked on. In most cases, they'll be responsible for supervising two to three large-scale projects at the same time. These projects can include installing a brand-new EHR system or improving IT security infrastructure. A project manager is able to oversee up to five to seven different projects at the same time when those tasks are relatively simple, such as minor software upgrades or hardware installations. This equilibrium guarantees that the project manager will be able to successfully manage resources, keep project timeframes in check, and provide the required results without sacrificing quality or attention to detail.

I am not sure there is a one-size-fits-all answer to the number and size of projects a project manager should oversee simultaneously. It is essential to evaluate the specific circumstances and factors involved in each situation. Striking the right balance between project complexity, interdependencies, resource availability, project size, the project manager's experience, and the support structure could help determine a reasonable workload for a project manager.