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Hi,
I don't recommend using these designs. While they work, they are not rigorously tested.
To answer your question; the trick with the v4 design is that it has a voltage doubler on board (LT1026), it's actually wired as a voltage quadrupler... to 9V in gets you up to 36V at the output (which is more than enough).
The "absolute maximum" input voltage to the doubler chip is 10V, so putting two 9V in series on the input would almost certainly fry the chip; the current is regulated to 2mA, so putting them in parallel isn't useful either.
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