MOS
From my understanding, the AFSC manager needs to approve your release before you can even apply to cross-train. For AD 62E (from 2006 - 2010, anyway), I remember getting a yearly e-mail stating that nobody will be released for cross-training.
As for transitioning in the Guard/Reserve, I think it's just a matter of finding a unit willing to send you to the appropriate school (and taking charge of any subsequent training).
Sir, I have an old school answer for you, not sure how relevant it could be today, but it may be able to bump it up to get you some more current responses.
I once crossed trained as a 63W in the mid 80s while stationed at Fort Sill, when we would prepare to go to the field, our motor pool was limited on mechanics, so most drivers that had assigned military vehicles would be taught/cross trained as light-wheeled vehicle repairmen (63W), and even though I was a 95B (MP) at the time I was granted the MOS as an OJT qualified from the command, it was much easier to get a second MOS that way back in the day. Of course they all but eliminated OJT capabilities in the mid 90s, so that went out the window for anyone who wanted a secondary MOS to ride with their primary.
Hope that gives you a little insight for now, until the SMEs can chime in for the current versions.
CAREERS is a first term Airmen program where you can apply from a list of jobs with "retrain in" objectives regardless of current AFSC "retraining out" objectives. The windows to retrain are tied to if you are a 4 or 6 year enlistee.
NCORP is tied directly to trying to level the force. You must be in a over manned AFSC with a retraining out objective and must pick from a list of AFSC's with a retaining in objective for your rank or projected rank.
The process is basically the same for both. You volunteer online via Virtual MPF, they verify that you are eligible to retrain and send you a package to accomplish. Physicals, testing, interviews, etc. All that gets sent back and you meet a board which approves you or disapproves you.
On the NCORP side, if your career field is over manned, they will select roughly double of personnel that NEED to be retrained (Based on newest date of rank) and these folks are vulnerable to be forced to retrain based on the needs of the Air Force if enough people from that AFSC do not volunteer. You do not have to be on the list to volunteer, but if you are fairly low (closer to #1) the more it is in your best interest to volunteer early when there are more jobs available then wait it out and be forced in to whatever is left over.
There are different rules outside of either of these programs for critical career fields (think SOF guys).
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