there is no requirement that a ground rod be 10' long nor is there a requirement for 25 Ohms.
a ground rod has to be only 8' long [250.52(A)(5)].
the 25 Ohms thing only comes into play if there is only one ground rod [250.53(A)(2)exception]. If you pound in 2 rods and it is 100 Ohms, that is fine with the code.
250.53(A)(3) requires supplemental electrodes (if required) to be not less than 6 feet apart. I suppose that if you threaded 3 ten foot long rods together and pounded them in you could make a reasonable claim that there were two rods at least 6 feet apart.
My impression is that the OP is also concerned with whether it would be OK to drive the original single rod deeper (using extensions) and then measure a resistance less than 25 ohms.
The code does not put any restriction on the maximum length of a rod electrode, so if driving the "failed" rod deeper got it below the 25 ohm limit, it would remove the need to drive a second ground rod regardless of the position.
I could see this being an attractive option if there were not enough free dirt space to drive a second rod meeting the separation requirements and no good opportunity for another type of supplemental electrode.
If you put the original rod in the middle of a 10 foot diameter opening in the concrete, then you could not just drive a second rod, you would have to drive two so that the separation between those two could be 6 feet or more.
Depending on the soil conditions, the single deeper rod could also provide a better ground, although the code does not care about that. Soil conditions where you could drive the rod 10 feet deeper would probably also be ones where the additional depth would help.
Only concern i would have is whether the threaded or screw coupling would be recognized as a good enough connection between the two rod sections. (Cadweld anyone?)
You could attach the GEC to the top of the lower rod section before driving it down I suppose.
