I got a Givi luggage rack and a set of sidecase racks for my V7III Special. They fit well and were easy enough to install. I decided to go with the Givis as I've used their sidecases and topcases in the past and had good experiences with them.

I had a set of old Givi E21s--they fit the new monokey racks. The E21s are plastic toploaders and convenient, and they don't add much to the width of the bike. The downside is that they are a little ugly. They're also cheap ($200 for two). They have been discontinued, but some may still be available; these have been replaced by E22s, which are more angular. The E21s:


I also got a set of Givi Trekker Dolomitis 30L. Givi says you should use these or the E22s for the V7III racks. These are much more substantial cases than the E21s. Downsides--side loading and no handles, so a little cumbersome to carry. Much more expensive than the plastic ones. Also, with these you buy two separate cases and you'll probably have to swap out some locks (more $) unless you want to carry two different keys for the sidecases. I think black ones have just become available. The Trekkers:


That's a Pelican case on the back. Big enough for a hat and some sunglasses., and very convenient. Lockable, too.
Rich A