Can I add a second circut using an existing ground and neutral?
If you want two breakers, you can't share a neutral and ground. The shared neutral and ground could be exposed to too much current, because they don't have breakers for protection, only the hot does. An example:

Assuming you've got an existing circuit with a 15 amp breaker and 14 gauge wire, you add a second 15 amp breaker, running a new 14 ga hot, and sharing the neutral and ground from the existing circuit. 

You have one load plugged into the "old" outlet, drawing 10 amps. 10 amps comes out through your old breaker and your old hot, the old 15 amp breaker sees 10 amps and doesn't trip, and the 10 amps goes back through your old neutral.

Now you plug in another load to your "new" outlet, drawing 12 amps. 12 amps comes out through your new breaker and your new hot. The new 15 amp breaker sees 12 amps and doesn't trip. 12 amps goes back through your old neutral. Now you've got a problem.

Your old 14 gauge neutral is now carrying 10 amps from the old circuit + 12 amps from the new circuit = 22 amps: thats more than the rated capacty. You haven't tripped a breaker, but you've overloaded your wiring. This is a very dangerous situation.