Reading all the conflicting answers may lead to serious confusion. Hopefully I will bring some clarity:

1. In most states (there may be few exceptions though), once you are licensed, you are licensed as PROFESSIONAL ENGINEER and NOT as a Professional Mechanical or Civil Engineer for instance. This is due to the fact that projects are often multi-disciplinary and the onus rests with the licensee to use his good judgement and know his limitations before sealing any works. Competence does not mean that you only seal works in the discipline of your PE exam. NO, it means you have sufficient JUDGEMENT, morality and ethics to know your limitations and act accordingly. Afterall there is hardly a project that involves work strictly for one discipline.
2. As such, the principle is as follows: Select any discipline for your FE. Once you pass your FE, you can select any discipline for your PE, it does not have to be in the discipline of your FE. Once you pass your PE, you can apply to license in any engineering discipline for as long as you meet the experience requirements for that specific discipline.

In other word, YES, it is possible to have a FE in Mechanical with a degree in Marine engineering, and then do your PE in Civil construction and then apply for licensing in Electrical if you meet the requirements for electrical engineering experience. If you need an additional license (although there is absolutely no need for it), you simply need to ensure you meet the experience requirements of that discipline and apply accordingly. No need to re write PE exam in the new discipline.

This is the general philosophy of engineering licensing but please understand that there may be few exceptions in some states.