When a word can not be classified as a noun/pronoun/adjective/verb/preposition/conjunction etc, it's classified as an adverb. So calling a word an adverb is not that helpful. Because an adverb in a sentence is used in various ways, and not all adverbs can be used the same way.
She was so much beautiful ... (INCORRECT)
In this sentence much is an adverb. Generally much as an adverb can't modify a plain adjectives (that is the case here, and that's why this sentence is incorrect). Though it can modify a comparative or superlative adjective or a past participle of verb.
He has not changed much.
A much loved family member.
The exam was much easier than I had expected.
Loach’s latest film is much the best thing he’s done.
Consider the following sentence -
Glad that you are doing so much better.
See in this sentence much is coming after so, but this sentence is not wrong. So your assumption that no intensifier can come after so is actually wrong. This sentence is correct because the adverb - much - there is used to modify the comparative form of good - better.