Two physical grounds??

If possible it would be best to tie the 2 ground rods together. Elizabeth is right about the possible difference in ground potentials. Otherwise in a worst case scenario IF you had a direct hit by lighting the voltage would jump from 1 ground to another. This happened to an old customer in Texas and the concrete floor between the 2 ground rods exploded. Again they took a direct lightning hit.

Try running a #14 awg to the outlet that your power conditioner is using, to a cold water pipe and clamp off to that. Swap out the old two wire outlet to a new three wire grounded outlet. The NEC allows for this and will provide an equipment grounding conductor for your conditioner. You can also run an addition wire to a driven ground rod if you would like. Don’t have any idea where the neutral (grounded conduction) receives it’s ground reference and might result in noisy ground loop, if so you can buy various products to combat that and the conditioner is much safer with the grounded outlet. Good luck. T. J.

Tio, on the one hand you mention that "the house outlets are of [a] type that accept a 2 prong plug." On the other hand, when raising the possiblilty of installing a separate dedicated grounding rod for the line conditioner, you mention the new rod would be "about 16 feet away from the ground rod for the electrical wiring for my house."

I assume that the outlet in question is wired with two wire ungrounded romex. Ergo, why there's only a two plug outlet available for the line conditioner.

I hope I'm not being simple here, but if there is a grounding rod for the house, to what extent is the house wired with three wire grounded romex. That is, the various line circuits all converge to one place, the fuse or circuit box, which in turn, I assume is tied into the house ground, as required by most electric codes. If most of the house wiring is grounded romex, then you could run a new grounded romex line from the outlet that is dedicated to the line conditioner to the grounded socket.

However, if the house is old (like mine), most of the house wiring may only be old fashioned ungrounded two wire romex. If so, I like Tjt's idea the best. Maybe that would work if you can fish the ground through the wall and attach it to the water pipe.