This is sort of bizarre. Who would think of such a thing? We all started out with a small blue book called Classic Italian Songs. It came in different keys. I got my first copy in a high school voice class where we sang, yes, "Caro mio ben." I very quickly graduated to choir.
I haven't wandered too far off the subject. Joyce DiDonato is singing them with a jazz ensemble backup. They are originally scored for figured bass. You knew that. So why can't a jazz ensemble realize a figured bass as well as the next person? This is in New York.
Now she's added one of those tango accordions to her ensemble. She wanders off to other songs after a while. It's fun.