How do I add a second wired garage door opener?
Yes you can, unless it uses a fancy communication board. If you can control the lights and the door from the controller you may not be able to simply splice the wire. I used doorbells to add openers at two other locations for a friend of mine. Even on a communication board you could solder in at the momentary switch on the board and effectively do the same thing. This is obviously a little more involving.