Firing glass in a kiln: can a piece be fired twice?

I have recently obtained a kiln for firing glass (the baby kind that you put in your microwave) and am trying to learn the art. I’m wondering, is it safe to fire a piece twice if you don’t feel it was left in long enough the first time? I’m just not sure if firing the glass causes it to change in such a way that it wouldn’t be prudent to fire it again.

I have no idea if we have any jellies with knowledge on this subject, but I figured I’d give it a shot as I’m having trouble finding information on the subject elsewhere.