In an interview PlayStation Lifestyle, Infinity Ward’s multiplayer Project Director Jordan Hirsh has stated that they are planning to have 10 total prestiges in Call of Duty: Infinite Warfare.
After each prestige, you will get an unlock token similar to previous Call of Duty titles. He also said in his response that the number of prestiges could increase based upon feedback in the future, but they do not have anything to announce as of now.
The Prestige system as it stands is pretty similar to what players have seen in the past and experienced. So as you Prestige you’ll unlock a Prestige token, and be able to bring over with you one item that would normally be gated via your player rank. Maximum Prestige right now that we’re planning is 10. That’s subject to change based on how things go in the future. We can adjust our experience curve, and we want that experience to be good for pretty much everybody.
SOURCE: PlayStation Lifestyle