Can I get a re-entry permit on a 30-day Visa Exemption extension in Thailand?

The original question asks whether it's possible to obtain a re-entry permit on a 30-day Visa Exemption extension. The consensus in the comments is that, while a re-entry permit can technically be purchased, it does not extend the stay in Thailand. Instead, upon re-entry, the traveler would only be allowed to stay until the original stamped date. Many commenters suggested that for shorter trips, it may be more beneficial to leave and return for a new 30-day exemption rather than buying a re-entry permit.