I was going through several boxes of accordion sheet music when I stumbled across this. I had seen several dual keyboard accordions on eBay and elsewhere over the years , but never a book on one.
Max Luttbeg was a wrestler from Russia who later went on to play the accordion on the vaudeville circuit. He later gave up on the system and came up with a freebase button system with 36 buttons but it is not clear how this was laid out.
The book dates from 1935 but a little research seems to imply the the first one built by Soprani was from 1931. Apparently only about 12 were built and not all by the same company.
From the pictures you can see that a second strap inside the bass strap has been added to give more control and keep the hand in one place.
Since you only have about two octaves on the left you have a shifter bar that allows you to shift up for chords (second image). Depending on what you play I think you might have needed this more than was convenient.
The book also has a pullout by Edd Clark for a "Model A" that was a compact version with 25 keys on the right and 14 on the lefty and was called the "duo-organ" and he explains that this setup makes it possible to play piano music as it was written.
This type of left hand keyboard is an idea that has come and gone several times ,and seems to make sense but in reality is pretty hard to master and does not bring any real benefit over the systems being used currently. Versions of accordions have been made with a inner row of bass buttons in the pattern of the black keys of a piano to simulate the black keys ,and a row of white buttons for the white keys , this has been in use for many years on a small number of ethnic instruments in Serbia and but has never really caught on elsewhere.