Alex Kurtzman and Roberto Orci are two of the writer-producers behind "Star Trek Into Darkness," but the team known as "K/O" is also producing the coming films "Ender's Game," "Now You See Me" and the Fox television series "Sleepy Hollow." Not to mention the sequel to "The Amazing Spider-Man," which they co-wrote and which is currently filming around New York.

Speakeasy talked with Kurtzman and Orci, who have been friends and writing partners for more than 20 years,...