Schools for members qualified in Submarine or Nuclear fields:
NEC Course Title Course #
EM-3376 Radiological Control Maintenance S-661-1023
EM-3354/84 Nuclear Propulsion Plant Operator-Electrician A-661-0013
EM-3377 Nuclear Planner Operation S-661-1022
ET-3376 Radiological Control Maintenance S-661-1023
ET-3377 Nuclear Planner Operation S-661-1022
ET-3353/83 Nuclear Propulsion OperatorReactor Control A-661-0012
ET-3373 Nuclear Propulsion Plant Maintenance SupervisorElectronics F-191-0010
MM-3351 Nuclear Propulsion Plant Operator Welder A-701-0015
MM-3376 Radiological Control Maintenance S-661-1023
MM-3377 Nuclear Planner Operation S-661-1022
I'm guessing here, but EM/ET/EM 3376 should be non-supervisory NECs. Generally, once advanced to E-6, the NEC is changed to EM/ET/EM 3377. I think the "337X" are surface and the "335X" are subs. Interestingly, there don't seem to be schools available for sub/surface ELTs (for subs, 3365/66. I don't know for surface, 'though I could find out easily or someone else will tell you, if you really want to know).
That's a short answer. When it comes time for you to make the decision, you can download MILPERSMAN 1510-020 from the web and that will list all the available schools. They may change. Sub MMs used to have an aux package school, but I don't see that on the current list.
buperscd.technology.navy.mil/bup_updt/ upd_CD/BUPERS/MILPERS/Articles/1510-020.PDF
For other STAR reenlistment details, there is MILPERSMAN 1160-100.
buperscd.technology.navy.mil/bup_updt/ upd_CD/BUPERS/MILPERS/Articles/1160-100.PDF