What is the maximum number of different keys that can be used when encrypting with...

Triple DES encrypts a message three times. This encryption can be accomplished in several ways. The most secure form of triple DES is when the three encryptions are performed with three different keys.

Source: KRUTZ, Ronald L. & VINES, Russel D., The CISSP Prep Guide: Mastering the Ten Domains of Computer Security, John Wiley & Sons, 2001, Chapter 4: Cryptography (page 152).