Is it possible to get a reentry permit at Immigration for a Special Tourist visa?
If yes, can the STV still be extended after returning back to Thailand?

You might be able to get a re-entry permit for the 90 day stay the STV allows or one of the two  90 day extensions it allows.

I assume you could extend the remainder of the 90 days you would get when entering with a re-entry permit unless it was your 2nd extension.

It is an interesting question. The general function of a re-entry permit is to create a situation where your current permission to stay is completely unaffected by your exit and return to Thailand. Thus, as long as you return before the current 90-day stay expires, you can proceed as if your overseas trip had never happened.