Can "with" be a conjunction?

Question

I am considering this sentence which I found from an SAT preparation book:

Although some designers are employed by companies, most work on a project-to-project basis, with each project taking anywhere from several weeks to several months.

The right answer was provided with this explanation below:

correctly uses the construction "with ... -ing" to join the final clause to the rest of the sentence smoothly.

If it joins the final clause to the rest of the sentence then it should be a subordinating conjunction, right?

But why in this site almost everyone claims that "with" can't be a conjunction Or maybe they are referring to a conjunction as a coordinating conjunction?

Answer 1

Although some designers are employed by companies, most work on a project-to-project basis, with each project taking anywhere from several weeks to several months.

No: "with" is always a preposition. It can't be a conjunction since unlike "and", "but" and "or", it can function as head of a constituent.

In your example, "with each project taking anywhere from several weeks to several months" is a PP with "with" as head and the gerund-participial clause "each project taking anywhere from several weeks to several months" as its complement.

Answer 2

This question came up on Stack Exchange English Language Usage:
"Is this a participial phrase, or a prepositional phrase, or both?"

After brushing my teeth, I go to bed

The first comment on the question seems particularly apt, as well as the answer and subsequent comments:

Stack Exchange EEU
"If the verb of the verb phrase is a participle, then it's a participial phrase. That's usually just a participial clause that's missing its subject (the subject is my when the predicate is brushing my teeth, and it's not present in the clause, but it's understood, like you in imperatives). When it comes after a preposition like after, it's still just a clause or phrase, but it's introduced by the preposition. You can consider it a prepositional phrase with a clause or phrase as its object, or as a subordinate clause or phrase introduced by a subordinator. It makes no difference. – John Lawler Dec 9 '19 at 22:49"

[Emphasis added.]