I suppose we should define our terms. One definition of doubling is that a person play various saxes and flute. Kudos to you guys, but that's out-those axes are all too close. It's expected (sorry, Rahsaan). Next, there are people who play credible piano, apart from whatever horn they play. You really have to play some piano anyway, so forget that. Then, there are those people who play "lower brass," meaning trombone and tuba/euphonium. This is a little more like it, as you have to master both slide and valves. But, still not enough (sorry Howard J.). And, in this context, singing just don't count.
No, I'm talking about musicians who master instruments from two completely different families: trumpet, reed, percussion and strings. With this, we've narrowed the field down from millions to just a handful. This is difficult enough to do that these people qualify as freaks of jazz nature.
I know I'll get in trouble with some folks by (they will say) putting a premium on virtuosity over expressiveness. Probably the key person in that conversation is Ornette and to that I say-sometimes yes, sometimes no, but without the technique, it's hit-and-miss. With the people I'm talking about, it's almost always hit.
I'll start with Ray Nance (aka "floorshow"), a man who played sweet violin, trumpet and danced, as his boss might say, divinely. Here's Ray soloing on violin and playing w. Duke's trumpet section.
Then you got Benny Carter, basically a contemporary of Nance, who, aside from writing and arranging, played beautiful alto and very credible trumpet-really knew his way around the instrument.
How about Jimmy Dorsey, who started on trumpet and moved to reeds, but managed to retain his trumpet chops. Here's a page of Dorsey stuff.
Bobby Hackett, whom we know as a fabulous cornet player actually started as a guitarist. I'm gonna pair him with Adrian Rollini, a fine bass sax player who doubled on vibes. Here the 2 of them are together.
Slightly younger than the above and on the Latin side was Mario Rivera, who played w. Machito, Stitt and many others. There was no family of instruments this guy did NOT play. Go here for videos.
I'm learning nobody likes a long post, so I'll end here. However, I got half a dozen more, including Gowans, Wetmore, Durham and one more, who I believe is the best of them all.
If you got anyone who deserves to be with this august group, let me know.