I assumed that adverbs modify only verbals (noun + copula, adjectives, verbs, however blurred their actual distinction). However, today I came across an entry in a grammar book [ISBN-13: 978-4789012959] on an adverb さらに （更に） that can (apparently) modify other adverbs, which proves this assumption wrong. Example sentence:
クローバル時代に向けて企業の国際化をさらに強力に押し進める必要がある。In our global age, we must promote the internationalization of businesses even more forcefully.
Here, it is explicitly stated that さらに modifies 強力に and not any of the verbals that follow.
My question: is there a special name for this class of adverbs (in that entry only さらに、もっと、より、なお、 and 一層 are listed)? Is there a list or some kind of way of identifying this kind of adverbs? Do such adverbs apply only apply to nouns that can take an adjective form (like 強力な)?
Edit: I've thought about it a bit more and it seems indeed some other extent adverbs can modify an adverbial if it's formed from na-adjective, e.g. そんなに深刻にX. Is that all there is to it, just treat a noun-form na-adjective + に as something that an adverb can modify?