Can I re-enter Thailand on a Special Tourist Visa (STV)?

The STV is a single entry visa. Valid for 90 days on entry. No longer valid for the 2 extensions you could get from it as the program has already finished.

I doubt you could get a re-entry permit from it but you may be able to. A re-entry permit will only give you permission to enter Thailand and stay until your current stamp. If you’re looking at January then a guess is that you wouldn’t have many days left on your stamp anyway.

Depending on your passport country you may be able to enter without a visa and you’d get a 45 day stamp on entry.

Go to your local immigration office and apply and you will get your answer.