This is a preliminary post -- I'll have one with photos soon.
I took a chance, for my 2014 Rocket III Touring, that I could install a top box straight away.
What I would prefer would be the Corbin Fleetliner, if I could afford it. At $1,850.00 shipped, it's just too rich for my blood.
Having had several Givi boxes on other bikes, I elected to purchase a Givi E55 Maxia III, from Revzilla.com, thanks to their customer service answering my questions.
For mounting -- everyone's question -- I'm here to tell you the Givi E251 generic Monokey mounting plate works just fine with Triumph-supplied rack on the Touring.
As others have mentioned, I removed the pillion back rest. There is a trick here, in that the posts of the back rest have threaded holes that take the bolts that both secure the backrest *and* secure the rack, with special spacers. As
@mport so helpfully pointed out, with the backrest removed, one must supply alternate attachment hardware. In my case, I retained the four OEM 12mm bolts, and there was enough room in the tubes vacated by the missing backrest posts, I chose to place two flat washers, a lock washer (I would prefer a lock nut -- but Lowes was out this evening), and a 13mm 8x1.25 nut.
So the Givi box and hardware arrived via UPS this evening, and several lazy hours later, the Givi E55 case is on the bike.
I also ordered a backrest pad for the box, on the suggestion of others here I ordered an Admore lighting kit for the box, a document holder (appears parts are missing and I have a question into Revzilla on that one), and the Givi optional red colored cover for the box, in some hopes of being a little more visible, and perhaps pickup the red of the bike (mine is the red/black two tone of 2014).
So, if you were thinking about a box, this is one sure, relatively painless way to add one.