Do all states offer Close Corporations?

Answer 1

The term "close corporation" simply means that the corporation is closely held. That is, it is privately owned by one or more investors. States do not "offer" this. In fact, almost all corporations are closely held. It is only a few that have "gone public" by taking the steps necessary to have their stocks broadly sold on stock exchanges. Some public corporations are buying their stock back in order to "go private".

You can become closely held in any state.