When we have a sentence like
I can identify with a company's products
Does the plural form of the "a" depend on the "company's" or on the "products"? The latter would mean that it had to be a "the" instead but I am simply unsure what word to refer to here.
Bonus points if anyone could recommend me accurate terms to describe this problem because I simply didn't know what to search for
There isn't a plural form of "a".
An article on a possessive phrase always relates to the possessor:
A company's products = the products of a company
The company's products = the products of the company
The choice of "a" or "the" has nothing to do with the products or their plurality. It is no different from a non-possessive example: normally, "the company" refers to a company which is already identified in the speaker's mind. "A company" refers to a company which has not so far been introduced into the discouse.
