If you run 2 grounds it would be: a) illegal in most places, and b) a sure-fire recipe for ground loop hums.
A ground is by definition at one point and that point is at the service entry. You are really not gaining anything and giving up a lot safety-wise with two or more separate ground points.
If your service is buried then your ground is most likely a ground rod. But it could be the water pipe also. Just bring the grounds back to the main panel the way it's supposed to be. Isolating the grounds from the receptacle boxes (if using armored cable) is all you need to do to minimize common mode noise from EMI/RFI.
A ground is by definition at one point and that point is at the service entry. You are really not gaining anything and giving up a lot safety-wise with two or more separate ground points.
If your service is buried then your ground is most likely a ground rod. But it could be the water pipe also. Just bring the grounds back to the main panel the way it's supposed to be. Isolating the grounds from the receptacle boxes (if using armored cable) is all you need to do to minimize common mode noise from EMI/RFI.