Dumbledore was very close to immortality.
I am not referring to the obvious ways like horcruxes or the philosophers stone.
Throughout the books we have seen 5 animagi McGonagall, James, Sirius, Peter and Reeta, out of these we have seen the first 3 character's patronus. The animal you transform into much like a wand, chooses you and you cannot control what animal you turn into, so it is safe to assume that the animal you turn into is your patronus. And we know that patronus can be magical creatures, like Dumbledore, his patronus is a pheonix. So if Dumbledore was to become an Animagus he would become a Pheonix. And as we know pheonix are immortal. This immortality could only be achieved by Dumbledore. He would have become extremely overpowered, immortality, healing tears, flight, flame travel which is just apperation, carrying immensely heavy loads or multiple people with them. It would also explain how he can apperate in and out of hogwats. It wouldn't have been tough for Dumbledore either, I mean Pettigrew did it.
I am not missing anything, am I?