Joining an existing corporation
Joining a corporation is something you can do by becoming a shareholder, and you can also be added as an officer by filing an amendment of Articles of Incorporation with the state of the business registration (in some states you don't even need to do that).
To become a shareholder, the corporation's bylaws need to be updated to reflect your corporate position and the assigned shares and responsibility details of your involvement with the company.
Technically speaking, yes you could use the corporation as an independent contractor for another company. I would definitely recommend discussing that option with the other owners/shareholders, as well as with your accountant to make sure there would be no special tax ramifications as a result of the additional income.
I hope you are able to find this answer to be helpful.