What is the responsibility of the supervisor and employee to prioritize duties and responsibilities? In taking on side projects that impacts an employee’s ability to keep up with workload?

It is unclear from the question whether the employee wants to take on new projects or the supervisor wants an employee to take on new projects.  Either way, it is the right and responsibility of the supervisor to manage and prioritize the work of her/his employees so that the most important work gets done.  On the other hand, if an employee is highly motivated by side projects, the supervisor may want to find ways to redistribute work within the unit to ensure that as many employees as possible get to do work that motivates them along with more routine work.  If this answer is not sufficient, please consult with Employee Relations.