This question leaped to my mind after reading the definition of basis, especially in this sense:
on a … basis the way things are organized or arranged; how often something happens (1).
In relation to the first sense, i.e. the way things are organized or arranged, the first thing that appears in my mind is adverbs. I was always taught by my teachers that adverbs, especially that modify verbs can be thought as 'the way we do something' (The italicized phrase is roughly the same translation said by my teachers in our native language).
All members of the committee work voluntarily.
Notice that voluntarily is an adverb. And as what my teacher taught me, it can be thought as all members of the committee do their work with voluntary. (Please note, although it may sound unnatural, this is used to understand how advebs work, not the literal usage. We don't say this sentence, but the my teachers use this to help me to understand.)
Anyway, back to my question, if my understanding is correct, then voluntarily can be replaced by:
All members of the committee work on a voluntary basis.
As I said in the title, I assume some adverbs that modify adjectives can be treated like this. I mean, any adverbs that have the same sense of (1). Is my assumption correct?