Can we extend our own core classes

[eluser]codeigniterzzz[/eluser]
Basically i have my own controller that extends codeigniter's controller:

class MY_Controller extends CI_Controller


Now my question is can again extend MY_Controller as another core class extension, for example:

class MY_Controllertwo exends MY_Controller


makes sense? In other words i want to another file called MY_Controllertwo which extends MY_Controller. And both are in the application/core folder.