The leading cast will also produce the project, which is slated to begin filming in summer 2023.
The fourth film will now be titled Beverly Hills Cop: Axel Foley.
Super Pumped is set to premiere on Showtime on 27 February.
Chloe Grace Moretz will play cult member Deborah Layton in the feature film.
Joseph Gordon-Levitt is to star in a new show exploring the rise of Uber.
Josh Gad, Nia Vardalos, and Jon M. Chu also tweeted about the news.