You should be able to do so.
go to the corporation page and scroll down.
there is an option to purchase shares of the corporation.
A CEO should be able to do so.
This does not mean you will succeed.
Someone must decide to sell you.
If you enter a purchase request, the price might go up and then, probably one of the other share owners, will sell at some point.
Frequently, some of the share owners are investment funds.
these will sell if the price is right for them.