I'm sure somebody's invented this. I'm just wondering why it didn't work or never caught on?
Edit: Ignore the apparent wind arrows. I forgot to rotate them when rotating the drawing.
As we all know, a ketch doesn't sail as close to the wind as a sloop. This is because the mizzen sail is in the wind shadow of the mainsail. Couldn't this be easily fixed if the mizzen sail is just shifted to the windward side of the boat, so that the relative position of the sails is more like a less close-hauled tack? If there are two mizzen sails, there's no bad tack, you just need to furl the leeward one, which is easy with roller furlers.
Obviously the second unused mast is dead weight and drag, but now I think of it, why do ketches even have a mizzen mast? Why isn't there just a backstay with the mizzen sail flying from it instead? A jib boom or boomkin could be used to allow the mizzen sail to hang past the transom. Twin backstays could allow the above twin mizzen sails to work.
The big advantages this might offer over a sloop with a larger mainsail are a lower centre of effort and higher aspect ratio sails for the same mast height.