But Mr Simmons, who has just completed a multi-city tour of Europe, is not satisfied. Already, his Rush Communications - named after his youthful nickname - is the second-largest African-American-owned entertainment company in the United States. Now 37, Mr Simmons has moved from music into film, television, radio and, most recently, fashion. His aim is not to be the number one black-owned US organisation but to be a big player by any standards. David Geffen, the entertainment magnate, is "like a mentor to me", he confided recently.
Although Mr Simmons has made his name and acquired the obligatory smart cars and Manhattan and Long Island homes on the back of the rap music of the ghetto, he was, in fact, raised in suburbia. Though he does not have a degree, it was while attending college in the Seventies that he became fascinated by hip-hop and the associated inner-city culture. At 19, he became a promoter and earned the nickname "Rush" through his high energy levels.
This enthusiasm and drive led him into managing and producing the likes of Kurtis Blow and Run-DMC, then rising stars of a musical form that he would be instrumental in "crossing over" into the mainstream. In 1985, he started Def Jam with Rick Rubin, a Jewish university student with whom he has since broken up. (Mr Rubin has now relocated to California, where he is perhaps best known for reviving the career of Johnny Cash on his American Recordings label.)
Two years after establishing the label, the pair signed a distribution deal with Columbia Records before becoming another casualty of the Sony takeover. Polygram, which prides itself on being an international company that can give unusual and creative people the room in which to develop, leaves him to carry on as he wishes, he says. Where Sony wanted him to concentrate on the music, Polygram is apparently indulgent of his multitude of interests, to the point where the president and chief executive, Alain Levy, wonders how he manages them all. Mr Simmons, meanwhile, says they are all related: the mystery is how Mr Levy handles all his responsibilities, he says.
While he is insistent that he and his acts remain "street" and "black", he also craves mainstream recognition. Having already backed four films, he has two scheduled for release next year. There are also television series, including one dedicated to comedy by black artists, and radio projects designed to promote his records.
Nowhere, though, is his ambition greater than in Phat Threads and Phat Farm, the fashion operations he started last year. A man who will talk animatedly about the differences between Ralph Lauren and Tommy Hilfiger's clothing, he is determined to see his line - which he describes as "classic American sportswear" - for sale in such top-flight stores as Bloomingdale's and Macy's.
But although fashion is a consuming interest - as demonstrated by his close friendship with the model Veronica Webb and frequent reports of sightings at fashion shows - it is not his only vehicle for expansion. He also enthuses about plans for a cafe or themed restaurant, which would, of course, feature his recordings and his fashion garments.
Keeping up with a man who makes such steady use of a mobile telephone that he has apparently run up $3,500-a-month bills is difficult. As he says, "I'm always launching a new business this week."
Nevertheless, he has managed to retain the core of his staff through a combination of loyalty to an organisation that has remained close to the culture which spawned it and that old standby, financial incentives.
Pointing out that the 60-odd people who work in Def Jam Music have a co-operative-style culture which means, for instance, that there is always somebody there at 2am, he says that they all have "a piece of it for the long haul".
He adds: "I want to make sure that everybody is as enthusiastic as I am. It means they can never be hired by others."
It is a principle that he is trying to extend to his other businesses. But he admits that a more pressing problem is finance, or rather lack of it. Though the label has made $51m in the first three months following the deal, Simmons still feels short of capital.
And it is here that his approach may cause him trouble. While wearing jumpers does not apparently do Richard Branson any harm, Mr Simmons combines his casual attire with being black. And there are signs that while black entrepreneurs can find a niche in the music business, they still find it tough to thrive in other fields.
He takes a robust view on racism - "Yes, I can't get a cab, but what do I need a cab for? I've got a Rolls" - but he sure would like some finance.
Complaining of feeling frustrated that his business is not developing as fast as it could because of a lack of funds, he adds that he would be prepared to sell a chunk of his company if it assisted his chances of expanding. "I don't want to own the whole operation," he says, pointing out that a strategic partnership would help to make an impact.