I am considering stacking rods so I will end up with 2 16' rods.

Why don't you just drive another 8' rod (IAW code) and be done with it.
You will be perfectly legal. If the earth doesn't really conduct
electricity then your "perfect groups" to the water table will not make any
difference.


Question is how close can these be without compromising effectiveness of
grounding system?

What are you trying to protect yourself against? Why sort of fault or
event will your "perfect" ground protect you against? The only thing I can
think of is if your "service neutral" opens. In that case, your ground
system could get charged (depending upon what is on and what is off in your
home) with up to 120 volts. But since your soil is a good insulator, it
really would not make any difference.