Ed Joffee has a great article in the Associated Musicians of Greater New York website about the history of woodwind doubling.
Multi-tasking has become a staple of modern living and is certainly a requirement for surviving in today’s music industry. The contemporary saxophone doubler represents the greatest example of this characteristic in music. While most people believe that the origins of this discipline occurred with the Paul Whiteman Orchestras of the 1920s, woodwind multiple instrumental performance dates back several centuries.