Goose neck and 5th wheel?

You could add rails and use any fifth wheel hitch, or utilize the gooseneck ball and use one of the turnover ball hitches. I have a rail mount Andersen Ultimate and I'm a huge fan of it, but they also sell a version that mounts on a gooseneck ball if you'd rather not mess with adding rails. You could also always add a gooseneck adapter to the trailer but that's a little controversial on this site. I was a little leery of the added stresses myself so I went with the Andersen instead, but my dad has run an adapter on his fifth wheel for over 20 years with no issues at all.

I love my Andersen Ultimate ...

I'm planning to upgrade my fixed gooseneck ball to a turnover ball sometime this summer if I ever get a spare afternoon.

Not sure which one you have but the B&W gooseneck is an underbed mount that you can use for the gooseneck and B&W makes what they call the companion 5th wheel hitch that mounts in the same hole to the gooseneck mount. So you can have both. The companion is removable so that you can use the gooseneck (two pins to remove the head, one bolt to remove the companion base takes about ten minutes to switch from one to the other). There are surely other brands that do the same.
http://www.turnoverball.com/products/single-point-attachment/companion-5th-wheel-hitch Again it will depend on what you have as to whether it can be done or not. I love mine for three reasons first I can tow both types of trailers, second the companion is a great 5th wheel hitch and third if not towing either I can have a completely flat bed with no rails for the other work the truck does.

Yes, you can!
In fact, a little research will show that there are quite good fifth wheel hitches that fit right on the gooseneck ball. I don't remember what they are, but I have seen them. In fact, my neighbor has one. Surely somebody will be along that has better information.