Is it common to work concurrently on projects with PIs other than your advisor?
It very much depends on your relationship with your PI, funding sources, etc. For example, a PI might discourage this kind of work if you are solely funded by one of their grants, wherein they need most/all of your research output heading toward a specific objective. On the other hand, it might be necessary to work on other projects if you have a gap in funding and need to take a research assistantship elsewhere for a semester or two.

In my own experience, even within a given department (or even a given PI), there's also a component of how interested a given student is in pursuing other projects, and how well they balance their time.