I was just there and I managed to get an item which was triple wrapped: It was a small tray which came wrapped in cellophane already, which the shopkeeper (very beautifully) wrapped in a paper bag and then put the whole thing in a plastic bag before handing it to me.

I didn't beat triple wrapped anywhere else, but 7-11 did sell me an "eco bag" which they wrapped in a plastic bag for me, before I had time and the presence of mind to tell them I didn't need the "fukuro" (plastic bag).