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Bennekom Double Move Chess. Move twice per turn with the same piece. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Rodrigo Zanotelli wrote on 2013-01-06 UTC
"All `double move' variants, I had known until then allowed the player to move different pieces."
I am almost sure there are 2 moves variants that only allow you to move the same piece.

But YES they aren't 100% like your variant.
If I remember one variant I saw allowed the player to make just one move (instead of the 2 ones) if he wanted.