I have so many: POS of 'many'
Dictionaries indicate that many here is a pronoun; it is certainly standing in for the noun questions.
If this is so, how could the adverb so modify a pronoun?
And yet it does. This is possible as "many" is basically an adjective, although its history is complicated and involves another word that was a noun.
https://www.macmillandictionary.com/dictionary/british/many Many can be used in the following ways:
as a determiner (followed by a plural noun): It happened many years ago.How many children have you?
as a pronoun: ‘Did he write any other books?’ ‘Not many.’ (followed by ‘of’): Many of you will be going on to university.
as a predeterminer (followed by the indefinite article ‘a’ and a singular noun): We shall not see each other again for many a long day.
as an adjective (after a word such as ‘the’, ‘his’, or ‘these’, and followed by a noun): He said goodbye to his many friends.
as a noun in the phrase ‘the many’: The few who behave badly spoil the enjoyment of the many.
The cause of this is that “many” started as two nouns mani (a large amount) and meinie (a household group of servants, etc.)
OED: II. As noun. [It appears that the phonological identity in late Middle English of many and meinie n. [Edit to add = a group; a crowd; a family or clan] in some regions led to a virtual merger of the two words. Hence many occurs from the 15th cent. onwards as a noun (used both independently and with a following partitive construction introduced by of ) […] [it] continued to be spelt and pronounced many, while the equivalent uses of meinie became obsolete, except in Scottish English.]
Variation in Old English in the vowel of the first syllable [is] caused by the substitution of the suffix *-īg for *-æg in very early Old English (compare -y suffix)
The –y suffix is used to convert a noun to an adjective. Might -> mighty; sugar – sugary, etc.
OED
A. adj. (determiner). Designating a large (indefinite) number.
- Modified by the adverbs as, how, so, too. (See also so many at so adv. and conj. 37†)
“There were so many sheep, I could not count them”
B. pron. and n.
I. As pronoun.
4.a. Modified by the adverbs as, how, so, too.
eOE Laws of Ælfred (Corpus Cambr. 173) xxxiv. 68 Gerecce hu manige þara sien.
1990 F. Weldon ‘Darcy's Utopia’ (1991) (BNC) 106 How many died ..in that particular disgraceful military episode, so that the workers should be duped yet again in the name of the Empire?
The example could equally be "So many died ..in that particular disgraceful military episode, and the workers were duped yet again in the name of the Empire.
†So (adv.)
- so many a. Such a (large) number (of). 1812 G. Crabbe Tales ii. 30 Believe it..glorious, to prevail, And stand in safety where so many fail.
The result of all this is that “many” is basically an adjective that is also a noun in a similar way to “The rich live in castles; the poor live in the fields.” And “This is government for the many, not the few.” Here it is clear what “many” means. An alternative view is that "many (noun/pronoun) is, in fact, "meine".
However, many as a pronoun (without a definite article), like other needs a referent: “We here are well-fed but many are ill” – Many what?
"So" when used to mean "to great degree" (2a1) is an adverb. Adverbs only modify "a verb, an adjective, another adverb, a preposition, a phrase, a clause, or a sentence [...]" (list has been shortened, click link for full list). If "so" is an adverb and is modifying "many", "many" must be one of these parts of speech.
It clearly isn't a verb, another adverb, or a proposition.
Clause, sentences, and phrases aren't parts of speech, so we'd still have to analyze it further if it were one of those.
From this non-exhaustive list, it could only possibly be an adjective. Looking at the entire list from the definition I quoted, it still seems like the best fit.
So, if it is an adjective, then what is "many" describing?
There are many sentences with understood subjects that don't always need to be stated. These are most commonly used in commands or as a response to a question. I believe that this is the case here.
To summarize, "so" is an adverb modifying the adjective "many", which is in turn describing the understood and unstated subject "questions".
I wouldn't describe "many" as a pronoun.
Do you have any questions? I have so many [questions].
Do you have any questions? I have many [questions].
Do you have any questions? I have three [questions].
Do you have any questions? I have a lot [of questions].
I can't think of any examples where you would use a pronoun and its referent noun phrase together (e.g. *"They Bob and Mary said 'Yes'."). It looks like ellipsis to me, so "so many" or just "many" would be a determiner.
The Stanford Log-linear Part-Of-Speech Tagger would classify many in that example as an adjective as @Kate Bunting mentioned in the comments:
Do_VB you_PRP have_VBP any_DT questions_NNS ?_. I_PRP have_VBP so_RB many_JJ .
VB Verb, base form
PRP Personal pronoun
VBP Verb, non-3rd person singular present
DT Determiner
NNS Noun, plural
RB Adverb
JJ Adjective
Source: https://www.ling.upenn.edu/courses/Fall_2003/ling001/penn_treebank_pos.html