A "casket set" is a lens kit with several different lens cells which all fit in a common barrel. Since seven different focal cells can be combined in 18 different ways (7 singles, 6 doubles with minimal FL difference and 5 doubles with 2 steps difference), carrying one of these was a lot easier than carrying corresponding "fixed focal length" lenses.
A triple convertible is a lens where front and rear cell can be used alone as well as combined, giving three different focal lengths in one barrel or shutter. If you add a third lens cell and put it all in a nice little box, you would have a six-focal length casket set. The "casket" refers to the box.
So while this seem to be the ansver to uor dreams what are the tradeoffs?
Well I see one in your pic in this thread.