Segue to another storyboard?

Yes, but you have to do it programmatically:

// Get the storyboard named secondStoryBoard from the main bundle:
UIStoryboard *secondStoryBoard = [UIStoryboard storyboardWithName:@"secondStoryBoard" bundle:nil];

// Load the initial view controller from the storyboard.
// Set this by selecting 'Is Initial View Controller' on the appropriate view controller in the storyboard.
UIViewController *theInitialViewController = [secondStoryBoard instantiateInitialViewController];
//
// **OR**  
//
// Load the view controller with the identifier string myTabBar
// Change UIViewController to the appropriate class
UIViewController *theTabBar = (UIViewController *)[secondStoryBoard instantiateViewControllerWithIdentifier:@"myTabBar"];

// Then push the new view controller in the usual way:
[self.navigationController pushViewController:theTabBar animated:YES];

From Xcode 7 onwards, you can do this graphically by using a Storyboard Reference:

Add Storyboard Reference to your storyboard. Create segue between ViewController and Storyboard Reference (ctrl + drag)

Then fill this fields.

Where "Tutorial" is "Tutorial.storyboard" file and "MainTutorialController" is your "Storyboard ID" field in ViewControllerSettings