This evening was stake priesthood conference, and afterwards, there were several ordinations, and I started thinking about how this was a little like support (which I've obviously been doing for too long).
The offices of deacon, teacher, and priest correspond to I1, I2, and "I3": preparatory stages where you have certain limited privileges and powers and have to prove yourself and practise.
Then, when you've shown you can handle those privileges responsibly, and when you've prepared yourself, you get supporthelp/get ordained an elder. At that point, you've got essentially all privs (except supportclose)/you have as much priesthood authority as any man on earth.
High Priests would be a bit like cat admins, then: they differ from supporthelps not so much in their privs (again ignoring supportclose) as in their duties: they have leading and presiding roles.