Two physical grounds??

Magfan, maybe they're really old?? Otherwise, I think most folks just slap a three prong into the outlet, but don't ground it.

As I mentioned in my post, my house is old, maybe built 50-55 years ago and was wired with 2 wire ungrounded romex. When we moved in about 18 years ago, we did a lot of home improvement and electrical work in the basement. While the basement ceiling was opened up, the electrician was able to rewire most of the 1st floor outlets with grounded romex. BTW, the electrician was licensed and his work was inspected by a township inspector to ensure all work was done in accordance with code.

FWIW

Back in the late 70s I lived in a house with 4 or 5 outlets TOTAL and push button/rocker switches for lights.
The service was Knob and Tube.....which was so old the code for it was written in Hieroglyphs. My dad, generally mello, freaked out when he saw it and 'bout demanded I move out........The house? One of the oldest in downtown Fullerton California and the very definition of 'fire trap'.

http://en.wikipedia.org/wiki/Knob_and_tube_wiring

I'm surprised. Your Romex may have been put in during a transition period between hard conduit and the newest 3-wire code. At least you didn't have Aluminum wire and fittings.
The house my dad built about '58 was all conduit which I think was the '3rd wire'.

Any of the 2-wire stuff left should be immediately upgraded to latest code. Some of the wiring...J-boxes, outlets and switches may be untouched for decades and ready-2-go.

I'm still a little......leery.....of multiple ground rods.....

Magfan, maybe it's is a local thing, but every licensed electrician who has been in the house for one reason or another says that as long as we don't mess with the old romex and don't overload the outlets, the old stuff is stable.

To undertake what I think you are suggesting, which is to change out the old 2 wire romex, would entail ripping the house apart. Most of the old wire is attached to the studwork. As I mentioned above, when the occassion arises, we always try to change over circuits to comply with modern code.

But what about the OP?? I wonder what his situation is. Btw, I'm not an electrician, so take this with a grain of salt, but I don't like the idea of two ground rods either.

If there are no other grounds, tying the two earths together is appropriate and does not create a loop if I understand what the OP is describing. The tie wire should be the same type of ground strap used from the service panel.

I'm not an electrician either. But you might be able to get a new ungrounded outlet somewhere. Another option would be to use a ground fault circuit interrupter, and I believe it needs to be labeled ungrounded on it. The extra ground rod is not an option, unless you bond them all at the service ground, per NEC, and local codes. Again I'm not an electrician. I am going by memory FWIW. That's not saying much with these middle age "senior moments". Gotta blame something.