Not 100% sure, but I think this would work:
- Create another OpenID (for instance at https://www.myopenid.com/)
- Go into your user profile page at stackoverflow.com
- Click the "new login" link, and follow the instructions to associate the new login with your newly created OpenID
- Go back to your user profile page and swap the ID's so that the new ID is the primary one
I hope it works that way.
Edit: this blog postthis blog post seem to confirm by belief.