You can design anything you want in any field you want. That just comes down to your knowledge base and what you want to do. If you are asking, can you use your professional license on something outside of the scope of your license, the answer is no. My PE is in Power systems. I can only stamp drawings related to power systems. I can not stamp anything in the EE realm dealing with "electronics, controls, and communications", or "computer engineering" things. Every field has its own professional license. As far as ME goes, there are 3 different fields for PEs:
Mechanical: HVAC and Refrigeration (PDF; new specifications for the 2017 exams)
Mechanical: Machine Design and Materials (PDF; new specifications for the 2017 exams)
Mechanical: Thermal and Fluids Systems (PDF; new specifications for the 2017 exams)
You can also hold different PE licenses if you want to put in the time (assuming you have your degree, 4 years under a PE) and pass the appropriate tests. As far as an electrician goes, I believe that is an apprentice / journeyman trade and not engineering.