How to change social security number
You can change it by visiting the Social Security Administration only if you have been a victim of sexual assault, or domestic violence. Make sure that you have valid documents. The process may be up to 6 months long. Check out http://www.ehow.com/how_4482314_number-new-credit-file-legally.html for details.
Join a Protected Custody/Identity or a Witness Protection Program at your local FBI building... Other than that pretty sure it'd be illegal.