Does LV has this shaped bag?

That bag in the picture is a similar shape to the damier illovo. I don't think the illovo can go across the body, but it is a shoulder bag.

Yup, first bag I thought of when I saw that is the Illovo. The thing is that one end of the strap can detach so you CAN add a strap in between...but I don't know how that'd work out or if it'd even look that great!