There's been a couple I know of. Les Darcy won the Australian Middleweight and Heavyweight titles but not the Light Heavyweight one (I don't think it was even around back then) as well as claiming the Middleweight world title. Ambrose Palmer and Ron Richards won the Australian Middleweight, Light Heavyweight and Heavyweight titles in the 1930s. Richards also won the Commonwealth Middleweight title (which was a big deal back then) as well as giving Archie Moore two hard fights in 1940. The other one I know of who won all three is Dave Sands.
Nice words on Darcy AFF. Dont forget he faught Bob Whitelaw for the Weltertitle also. Losing over 20 rounds, and deafeating Whitelaw the second time around via KO,although Darcy weighed at the Middle weight limit. Not all agreed with Darcy being National M/W champ, as he's taken the 'Australian' version of the world title before fighting Mick King. His claimancy to National M/W honours is questionable, even though listed. Other than Ambrose Palmer, Ron Richards, Dave Sands and Tony Mundine... you could almost add Wally Carr Wally claims to have 'toyed' with Dave Russel during their bout.
Russell did get the points over Wally though, and perhaps surprisingly IMO. Dave simply couldn't jab, and Wally probably had more ability in one finger than Dave had in total. Still Dave had some pluck, could bang away and was probably 10kg heavier.