Can an adverb modify itself

Yes, using homonyms. But it is exceedingly rare, and often confusing, when a Word used as a verb or adjective is modified by itself as an adverb.

Example: "One cannot fast fast; its meaning is in its duration."

(here fast is a verb meaning to not eat, and also an adverb meaning quickly)

Much more common, and still likely confusing, is a Word used as an adjective to describe itself as a noun, e.g. "The set set (established, group) may diminish in size." It is even possible to use the same Word three times in a row. "The second-second second surprised everyone." (Someone seconded a motion just two seconds after it was proposed.)