What are other adverbs that can't be negated just like "sometimes" and "occasionally"?
I don't sometimes drink milk.
I don't occasionally drink milk.
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No adverbs of frequency can be negated the way you suggest. This is because an adverb of frequency defines how often you do something. When you define how often you don't do something, you are actually defining a break in a routine, and we would instead refer to the break as something we do rather than something we don't.
For example, "I sometimes drink milk" means you only drink milk occasionally. The opposite to that would be to say "I drink milk often".
However, if you said that you always drank milk - perhaps suggesting that it is your drink of choice, or that you drink it every day - you could make an exception to this by saying "sometimes I don't drink milk", which would mean that there are occasions when you drink something else. It works with 'occasionally', too, and likely most adverbs of frequency could be used in this negative way.