Most Motorola phones are modular, allowing for interchangeable cases. However, not all Motorola phones are changeable. Learn more about the details of your specific phone to determine whether or not its case can be interchangeable. Motorola's official website has details about each phone.
Certain Motorola phones like the Moto X, Moto E, and Moto G have interchangeable cases. However, some Motorola phones like the Motorola DROID series do not allow for case changing. The DROID Maxx, the DROID Mini and the DROID Turbo series of phones are examples of this. The Nexus 6 is also restricted to its default case.