He moved the family to New York for a time in the sixties to absorb what he could from the centre of the jazz world, eventually switching to the valve trombone to follow in the footsteps of American jazzer Bob Brookmeyer, another mentor. He hung out at the legendary jazz bar, Jim and Andy's and went on the road with Canadian jazz great Maynard Ferguson.
Those were heady times. But McConnell soon gravitated back to Canada, as he would throughout his life, for the sake of family and friends.
His son Brian knows all about the big names his father played with over the years - Mel Tormé, Sarah Vaughan, Doc Severinsen, to name but a few - but to him, Rob McConnell was mainly just his dad. "He was a great dad, a very great and supportive, loving dad," he said.
Brian's favourite memories include sitting in sound booths with the engineers as his father recorded commercials for the likes of Pontiac cars and Wink soda pop. As with most Toronto jazz musicians of the time, studio work was the bread and butter that allowed McConnell to pursue his less remunerative musical dreams.
When he wasn't in the studio or leading the band, he spent long hours at the piano in his study at the family's home in Markham, Ont., absorbed in composing and crafting the jazz arrangements that would make him famous.
"There was never a wasted note in any of his arrangements," notes Bill King, the artistic director of the Beaches Jazz Festival in Toronto, and another long-time fan. "He would take something everyone knew as a standard and then sort of rewrite it. He would take it in a different direction, and the arrangement would grow organically into something surprising, something not heard before."
McConnell also wrote his own compositions, some of which ended up on the well-selling Boss Brass recordings. But he always saw himself mainly as an arranger.
"He was a great arranger, and he knew it," Thompson said. "He was a great composer, and he didn't know it. I was always sorry about that."
McConnell formed various sized bands that played park concerts, CBC variety shows, jazz festivals, the CNE and the occasional club.
Then in 1968, he was in the mood to do more. He approached radio executive Lyman Potts, founder of the Canadian Talent Library and a Canadian-content pioneer, and said he could provide the band if Potts could come up with the money to make some recordings.
It was a deal, and the Boss Brass was formed. It comprised 16 pieces - trumpets, trombones, French horns and a rhythm section. The first records were arrangements of the chart toppers of the day - the kind of music that would guarantee lots of radio play.
But while the group was getting known on the radio for pop tunes, its main purpose was always jazz. In 1969, the Boss Brass made its debut at the plush Savarin nightclub in the financial district, wowing audiences from the beginning and drawing huge crowds to hear McConnell's arrangements of the big-band repertoire.
Those who followed the jazz scene in Toronto at the time no doubt remember the night in 1970 when saxophonists Moe Koffman and Jerry Toth picketed a gig with placards saying "Boss Brass Discriminates Against Sax Players." The publicity stunt worked and a sax section was added. Eventually, the band grew to 22 and sometimes included more players sitting in.
Between 1968 and 1998, the Boss Brass made more than 30 recordings for such labels as Concord, Pablo, MPS, Sea Breeze and Innovation. The band earned Grammys and Junos and a wide international following.
It band made its U.S. debut at the Monterey Jazz Festival in 1981 and performed with Mel Tormé in 1983 and again at the Playboy Jazz Festival in 1986. Tormé, who had sung with virtually every famous big band through many decades, thought the Boss Brass was the best around. He came to Toronto to record with the group in 1987 and was on record as saying it was one of the highlights of his musical career.