There is a legal concept of "corporate personhood", but it has nothing to do with "being people", it's a legal term of art. For example, it makes it possible to sue a corporation instead of trying to sue each of its shareholders and executives individually. And it wasn't used in Citizens United v. FEC at all.
I don't like it, I really don't agree with it, but the reality is that's what it would likely take to overcome counter arguments in favor of continuing corporate personhood. As I mentioned, it might be tolerated if it came with tax exemption, in leiu of new taxes against corporate/stock loans and more taxation on profit distribution.
You don't lose your right because you act collectively, though some things get conceptually awkward.