Hi, Marty. Possible, yes. Easy? Depends. All you have to do is run 2 wires from either the doorbell pushbutton to where you want to mount the second bell. That is the rub. In our house, that would mean some big time snaking and wall patching.
Electrically, it's not hard at all. The pushbutton just breaks one of the two wires going to the bell. Push the button, you close the gap in one of the wires which completes the circuit and rings the bell. It's easiest to run another 2 wires from your present bell to the second bell. Or you can cut into the pair of wires that run from the button to the bell anywhere--if you can find them.
With so many possibilities, let us know more about accessibility of your system and perhaps we can guide you better.