The Third Order Grades
Babe of the Abyss
If the Grades beyond the Adept Grades are truly a separate Order on itself, there should be a probationary Grade that serves as an entry to it (much like Neophyte serves for First Order, and Portal does for Second Order).
In the AA, Aliester Crowley placed a new Grade between Adeptus Extemptus and the Magister Templii Grades; he dubbed this Grade "Babe of the Abyss." For simplicity, we will use his term.
The goal of the Babe Grade is to learn how the stigma of death is overcame, and how the abyss that separates the infinite and finite, the unmanifest and the manifest. They also study one of the major mysteries of the path of return and redemption.
Magister Templii
"Master of the Temple"
The Magister Templii Grade is associated with the highest sepiroth of the Pillar of Severity (Binah). In theory, the Magister Templii has reached the limits of the possibilities of the Pillar of Severity and has started to learn the ultimate mysteries of form.
Furthermore, this Grade studies the underlying symbolism and energies of the Adeptus Major Grade ritual.
Magus
Much like the Magister Templii has reached the limits of the Pillar of Severity, the Magus reaches the edge of what the Pillar of Mercy has to offer. The Magus spends much of their time coming to a greater understanding of the Adeptus Extemptus Grade ritual.
Ipsissimus
"He who is most himself"
There is some debate on whether a living person can attain any of the Third Order Grades, not alone Ipsissimus.
Assuming that the Grade of Ipsissimus could be attained, it would be the gateway to complete union with the divine and the unseen forces of the universe.
Symbolically, the Grade of Ipsissimus would represent the redeemed man, the regaining of the Garden of Eden, and the original receiving of the gift of Kabbalah.
Whether or not, anyone can actually attain the Grade, the concept behind the Ipsissimus Grade reflects a very real phenomena.
Paul Foster Case, in his book The True and Invisible Rosicrucian Order, talks about the phenomena:
"In any circle of human beings, the dominant center is person who has the highest degree of self-realization."
Case goes on to state that this person's will imposes itself on the rest of the group, even if they don't say a word (297-8).
This phenomena shows up both in exoteric and esoteric groups. In every gathering of human beings, there is one person who can be considered that group's "heart and soul," the ruler of that group of individuals.