Some days the halls were fused with a caustic scent, as of cleanser applied too liberally.
In the above sentence, I don't know how to parse this "as of". I know it is used like "like" in this sentence, structured in this manner; scent of (or that is of) cleanser. But I just cannot figure out a legitimate way of filling the gap between "as" and "of". I tried a few, including:
...caustic scent, as it is of cleanser applied too liberally.
...caustic scent, as caustic scent of cleanser applied too liberally.
But these don't seem to work quite well, because "as" here should have been used as conjunction, serving the purpose of "indicating by comparison the way that something happens or is done", like this example:
"Dress as you would if you were having guests"
For a conjunction to be used, a clause has to be used after a conjunction, or at least in the case of "as". But after "as" in the sentence above, there is no verb or any modal verb noting the verb phrase deletion, highly suggesting that "of cleanser applied too liberally" is not a reduced clause, but only a noun.
So, how should I parse it? What is the word that should be in the gap between "as" and "of"? Is it even used as a conjunction?