Prosecutors allege the singer abused the teenager after meeting him at a Chicago McDonald's in 2006.
They want evidence of this, and other alleged but uncharged crimes, to be heard at Kelly's trial in August.
Kelly denies ever abusing anyone, and his lawyers have not responded to the latest allegations.
The Grammy-winner, real name Robert Kelly, is set to face trial in New York next month on charges including child sexual exploitation, making indecent images of minors, racketeering and obstruction of justice.
The charges involve six unnamed women and girls.
Now, prosecutors would also like jurors to hear about about more than a dozen other people they say Kelly abused, threatened or mistreated.
They include a 17-year-old boy and aspiring musician, whom Kelly allegedly met at a McDonald's and then invited to his Chicago studio.
After offering to help the boy with his music career, Kelly is said to have later propositioned and had sexual contact with him while he was still underage.