the persons in the corporation would not lose their vote. the corporation is just one additional person, meaning someone could create multiple corporate persons and multiply their vote (at least, in OP's hypothetical scenario)

I think you misunderstand the argument made by many who say "a corporation is people". "Corporate personhood" is just a word the left uses to make it sound crazy.

In reality, the argument is that you can't restrict a corporation's speech because using a corporation to speak is merely a form or method people use to speak.

You could speak via billboards, grass roots organizations, a radio show, lettets, or even a company you own.

The government can't curtail your speech no matter the method.

more generally, "corporate personhood" in US law, going back to at least the 1790s and in other countries going back even longer, serves the legal purpose of establishing that when people work together to do something under the "corporate" banner (which allows them to have a succession of members working toward a common goal and pooling resources), they retain rights like speech, property ownership, and ability to enter into or terminate contracts including hiring and firing employees. This connects to the idea (expressed by chief justice Marshall) that "The great object of an incorporation is to bestow the character and properties of individuality on a collective and changing body of men."

Sheesh I wish I had read your response before posting my own. This more succinctly captures what I'm trying to say.

Right, and that's what I'm saying is flawed logic and a bad analogy for speech rights. Putting people in different groupings doesn't change how many votes they get, and saying that "corporations are people means corporations get their own separate vote" is a gross misunderstanding of what we're talking about. When someone says "corporations are people", they're saying "corporations are simply a grouping of people taking an action together".

The people who comprise a group have no extra vote to give: if two friends and I form a group, a new vote allocated to the three of us doesn't magically materialize. By contrast, since there is no quota for speech per person, two friends and I can form a group (eg, an advocacy group) and tomorrow go down to Union Square (or buy airtime, or hand out pamphlets, or stand on a street corner) and engage in whatever legal speech we like, collectively. The claim is that if that group of people happens to be given the structure "corporation", that doesn't automatically allow for infringing on the rights of the people within the corporation to engage in legal speech.

Again, I'm making no statement as to whether I think this approach is wise or good for society or not, but it's astonishing how common it is to see people who completely don't know what they're talking about on this issue and yet are somehow super passionate about it.