The Navy trials that the Caliber Reduction Board ran led to the 6mm Lee Navy, but they tried several other cartridge case types, both rimmed and rimless.  There were two forms of 6mm Remington, both short and fat and rimmed.  There were at least two forms of 6mm Luger, a rimmed case for a German rifle or two.  And there was a rimmed version of the Lee Navy, recommended by Winchester because it would function more reliably in Gatling guns.  I have seen samples of all those cartridges, but they are definitely rare.