If the neck of your shirt or jacket doesn't fit you, you're shit out of luck. That's the one part of the garment that's just stupid to alter. Leave the top button undone if the collar's too small. Leave the collar undone if it's too large as well. Invest in bowties that look equally attractive tied as untied. Unlike pants, moving the button over won't do anything but overlap your collar, throw off the rest of your buttons, and make you look stupid. Both sides of the collar are visible and made to meet in the middle. Pants waistbands are made to overlap with one side covering the other. Waistbands can cover more or less; the center of a shirt can't move.
You can make a collar narrower but not wider.
On a jacket, this involves undoing some of the lining, resewing the collar edge, and re-doing the lining. If the original collar is hand tailored and beautiful, leave it be or take it to an old-school tailor. Hand tailored collars (and lapels) have a roll and body that can't be replicated by modern tailoring techniques (mostly, they involve sewing the layers of the collar flat and thus the finished product is flat).
On a shirt, this involves a lot of work for very little difference. There's lots of stitching to be undone, all of it on areas with minimal seam allowance to begin with, and it's generally a fiddly process. If you love the shirt, it can be done, but don't expect your tailor to be happy about it.