Do the Three Energy Systems work independently of each other; or do they overlap with one another, each one contributing to different degrees as the body performs physical activity?

Overlap to some degree ...

Explanation:

The three energy systems work co-efficiently to provide body with energy according to the extent of physical activity. Not only these three system work together but the superpose each other to get the cycle keep on going. ATP is the main energy currency made by these systems. When one system produces enough currency, the same currency is again utilized for body as well as for the system to keep on going. These three systems include The Glycolysis, The Immediate Energy Transfer System and The Oxidative System ...