You can upgrade anytime up until the end of the fifth day of use on your ticket (as long as it's within 14 days of the first use, of course). FWIW, this rule is now true even for Disney resort guests - you used to be able to add an extra day up to and including your checkout day, regardless of remaining entitlements on the ticket, but that changed very recently.
Any theme park ticket window or Guest Relations location can handle the upgrade process. I honestly have no idea if resort concierge desks can do it these days or not.