Can I make a UIView transition to itself?

Sure, why not?

Let's say you have a UIViewController and you want the base view to do a CATransition from itself to itself:

- (void)doTransToSelf {
    CATransition *anime = [CATransition animation];
    anime.type = kCATransitionPush;
    anime.subtype = kCATransitionFromRight;
    anime.duration = 0.5;

    UIView *mySuper = self.view.superview;
    [self.view removeFromSuperview];
    [mySuper addSubview:self.view];
    [mySuper.layer addAnimation:anime forKey:nil];
}

Or, changing this to work on a subview of self.view is trivial.

So, why would you want to do this? In my case, I have a collection of data objects and a UIView that is the user interface for editing one object. When the user is ready to move on and edit the next object in the collection, the user interface doesn't substantially change, I'm really just changing the data object that is the target of the user's edits. So I want to re-use the same view with the same set of IBOutlets, and just do the transition as a visual cue to the user - "okay, you're working on a different object now."