You can do so. You just have to add the code below to the place/action where you want to change the rootViewController.
//First dismiss your currently loaded ViewController
[self dismissViewControllerAnimated:YES completion:nil];
//Get the keyWindow of the app
UIWindow *window = [[UIApplication sharedApplication]keyWindow];
NSString *identifier = @"Your_Identifier_Name_For_ViewController";// this is the identifier name(Storyboard ID)
// of the AnotherRootViewController
// which you have to set in your Storyboard
// as shown in the figure.
//Now create an object of the AnotherRootViewController
AnotherRootViewController *newRootViewController = [self.storyboard instantiateViewControllerWithIdentifier:identifier];
//Finally set your newRootViewController
[window setRootViewController:newRootViewController];
And make setting of AnotherRootViewController to Storyboard as shown in figure:
Let me know if it satisfy your requirement.