I just found this:
http://www.njmp.com/how-do-i-get-on-track.html
The next event is Jul 22 then Aug 30. There are several different sessions that allow you to use your own car. The highest level is "hot laps" for qualified drivers
"Just like the Hot Laps with Instructor experience, here is a chance to bring your own performance car on one of our 2 world-class road tracks. Instructors and drivers with qualifying HPDE experience or competition licenses only for this run group. This program will allow for advanced passing rules at speeds up to 150 mph!This is a chance for the tenured drivers to hone their skills. This is also an opportunity for instructors to take their students for instructional right seat rides"
For the non trained there are 2 sessions progressive laps and hot laps with instructor.