... do we know if Wheatstone, or any other English maker, ever managed to double up on reeds to get octaves or wet tuning, like a typical chemnitzer or bandoneon?
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Yes, George Jones may have been the first, as he claimed to have in "1859 made the Celestial English and Anglo Concertina." (At the time "Celestial" was being used to describe a tremolo-tuned German concertina, and "Organ Tone" an octave-tuned one.)
As Chris has mentioned, Lachenal's produced a number of their "Accordeaphones" in the early 1930's, and even Wheatstone's made at least one triple-reeded concertina, an enormous MacCann duet that used to sit on top of Jim Harvey's sideboard (minus its reeds, which Tommy Williams had "cannibalised").
I would suspect that the 1931 "Accordion" Crabb concertina, which Geoff mentioned, may have been double-reeded, and certainly they custom-made a brightly coloured trio of double-reeded instruments in the '60's, here's a photo of the red one :
I have also seen one made by Colin Dipper, and I'm sure that there have been others ...