Can I Apply for a New Non-O Visa While Current One is Still Valid?

why don't you go last border run before your visa expired? you still get another 90days +60days extension if you want.

Anyway, both (the current one and the new one you are going to get) of your visas would be issued at Savarnaket, check with that consulate if they can cancel (or void) old one and issue you a new one. I'm saying this because some consulates mention that only issuing consulate would be able to void issued visa and you need to do it before you apply new one in case you need new one before expiration. Though I had never read any report like that, maybe you need to check with them.

Otherwise, as Robert says above, not possible to have two (or more) active visa in one passport.

Officially NO, you can not have multiple valid visa's inside a passport You may try and see if the Consulate wants to give you leniency