How to set current User class in controller (inherited from the main User class)

Question

In my controller I want to access the extended class of the User class, but only in this controller and not in other controllers. Is there a way to set the User class per Controller?

The background: I have a global User Class which is for the whole project. In a special Controller I want to have access to an extended User class, so I can give the User class another relationship. This relationship is not necessary for the rest of the project.

Models:

class App\User extends Authenticatable implements MustVerifyEmail { ... }

class App\Special\User extends App\User {
  public function myMethod(){}
}

Controller:

class SpecialController extends Controller {
  public function myFunction(Request $request){
    // This $user should get the App\Special\User
    $user = Auth::user();
    $user->myMethod();
  }
}

Does anyone have an Idea how I can get this, without setting the global User class to the special User class and without putting myMethod in the global User class?

Thanks.