Why not?
Company ownership is already broken into shares. There’s no law of nature or logic that dictates how those shares are distributed. There are all sorts of ways to divide them between capital investors, labor investors, even outside stake holders like customers and suppliers. Any individual may be a labor investor in one company, and a capital investor in others. That one person would embody both your bourgeois and proletarian classes.

Again large economies are too complex for simple, clean, universal solutions. Their complexity necessitates more complex thinking.