Personally, I would call something a "success" when it spawns a media franchise of any sort. This is a business after all. Nura spawned anime, games. Same with Beelzebub and Reborn. Rookies spawned a TV drama and a movie. Psyren had nothing but the manga. In my books, I wouldn't call it a success.
You never said about spawning different media outside anime and exactly being "cancelled" and having no "anime" was your point. And Beelzebub don't have a game (Oga appear in J-Stars Victory, but that's not a Beelzebub game). Nura did had a game, it was bad, but had one. Psyren had 2 light novels, do they count for you? But considering you count Rookies TV and movie as separate, then the novels for Psyren should be counted too -> different media than manga -> success in your eyes.
It doesn't really matter if something have spawned multiple media projects. All it matters, if it earns enough money to be a success. And in Jump anything that ran for 3 years was obviously earning them enough money to keep it. There are franchises that have spawned multiple different media type projects, yet they earn less than some that haven't spawned different media project. So different media project is by no means definition for success. If we go outside of manga world, there are some failed franchises that did very poor, but ended up getting different media project in hopes for success, but failed again. In your eyes those would have been success? Strange...
