Hi @DrTerriC,
This seemingly easy question could probably get complicated quickly... I think a lot of it is going to depend on exactly how your assessment process(es) are designed.
I can tell you for my institution, our assessment process for GenEd is designed around specific outcomes assigned to each course (not directly to specific grades/assignments/activities). Instructors can attach the outcomes to appropriate assignments/quizzes in the course as they see fit. At the end of the term, I (as our Canvas admin) provide an outcomes report to our assessment coordinator, who then does a bunch of stuff in Excel to evaluate and report on the data in a nice readable way to our campus leadership.
Maybe our method would work for you, but if your assessment process is based more around grades, activities, time, etc, you'd definitely need a different approach. Hopefully others will see this and chime in as well.
-Chris