Many years ago, EasySaabre on Compuserve (see, I told you it was many years ago) would offer UA 1 for LAX-JFK as a three stop. Of course, UA1 and UA2 were the round-the world flights, so the routing was LAX-HKG-DEL-LHR-JFK.
Sadly, it wouldn't price out in F to be the same as UA 2 LAX-JFK nonstop....