The company made a major league effort to get the contract.
Calatrava is a major league architect.
You can't be so casual. You're in the major leagues now.
He made a real big league play.
Bill accidentally faxed sensitive documents to our competitors, and such a major-league mess-up could only be dealt with by firing Bill.
... 75% of pitchers in the major league ...
... sophistication. The example I like to give is Major League Baseball. For a hundred ...