I found that the only way out of the Google perma-ban was to grow large enough to have them call you instead. Their representative - apparently surprised by the fact that my site was banned - clicked a couple of buttons and the ban was removed. The account even had the hundred dollars that was there when I was banned years earlier.
How big do you have to be?
Accounts are probably attached to your identity (SSN, domain, etc.)
The only way to get another adsense account is if you form a new legal entity.