What if my seller wants to “refresh” a listing with a new MLS number?

You may re-list/re-enter a property but ONLY if you obtain a new listing contract.
If you signed a contract extension amendment, you may not re-enter it in GNMLS for a new MLS number as that would be against the MLS rules. You would simply go to Autoload > Change Listing and enter the new expiration date.

GNMLS Policies & Procedures:
V. Listings, Item C:

A new listing contract is required to obtain a new MLS number and reset days on market information.
See the complete Policies & Procedures HERE