Redressing a controversial subject...

The top is what i belive you are suggesting. That would require 24v and would leak current to ground through the secondary which would destroy the coil

Bottom is in parallel which would double your current output but there would be no reason to go about it


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The way you have drawn these it is more of a current doubler (except the first I don't think that works as drawn). I am thinking more in terms of a voltage doubler/tripler from the OPs description.