The brain anticipates the contact and prepares itself for this contact. Our brains can distinguish between expected and unexpected sensations. Since the feeling of surprise, unease, or panic is taken away, the body does not respond like it would if someone else was doing the tickling. So I'm sorry to say that you won't be able to bring on the uncontrollable laughter that tickling causes on your own.
That's Real Question Part A. Part B is....can you specify a particular "other personality" to be tickled, or would ALL of the other personalities be tickled at the same time?
But the real question remains...If you have multiple personalities, can one personality tickle the other?