The Stone is about a spiritual journey. That much is clear. Many of the characters that Charles Bobuck encounters seem to have religious significance: They are compared to angels, or the Buddha, or God, or a monk, etc., and they appear to act as spiritual guides for Charles. Maybe it is no surprise that many characters are doctors (e.g. Dr. Hill, Dr. Coleman, Dr. Hulbert, Dr. Wasser, Dr. Savioli), and that Charles (presumably) dies in the end. If this whole opus is simply Hardy Fox's way of retiring his Charles Bobuck persona and leaving his past behind, then he sure put a tremendous amount of effort into it. There is a lot of theology here.
Where to begin? At one point in the story,
The Book of Ibbur is introduced. I think "Ibbur" provides the biggest hint as to what the whole story is about. According to Wikipedia, Ibbur is "one of the transmigration forms of the soul and . . . is the most positive form of possession, and the most complicated. It happens when a righteous soul decides to occupy a living person's body for a time, and joins, or spiritually 'impregnates' the existing soul . . . to complete an important task." With this definition in mind, the righteous soul that occupies Charles' body is likely the ghost described in Chapters 1 and 2:
"From nowhere, a naked man appeared at his side and purposely sat down on top of Charles head until the results appeared more like a centaur than any human ever seen. At one point the mans **** perfectly aligned with Charles' nose. The resulting image was quite funny though no one was around to appreciate it but Jesus hanging there on the altar. Then he stretched out, slowly being absorbed into the sleeping human, until all that was left was a sleeping Bobuck." - Chapter 2, The Stone
Notice that the moment the ghost enters Charles' body, he hears Dr. Hill's voice. The narrative then immediately flips from 3rd person to 1st person. Here we can get an idea of how the plot is structured. The "Father Peter" reality is Charles Bobuck's external world (which may not necessarily be the real external world), while everything else, described in the 1st person, is Charles Bobuck's inner world. The spiritual journey begins when the ghost enters Charles, and speaking as Dr. Hill, guides Charles to his ultimate purpose.
And what is that purpose? Well, the book is titled "The Stone." Compare the following two quotes:
“Congratulations, your rock is a piece of liver.” - Charles Bobuck in the first chapter
vs.
"Finally, the stone that was not a piece of liver. The stone was not a piece of liver, it never had been." -Charles Bobuck in the last chapter
The purpose is to see the stone as a stone, and not as a piece of liver. This alludes to the Buddhist parable Charles recalls in Chapter 3:
"I had been reading about the life of the Buddha before I went to bed, and one passage kept coming back to me in a thousand variations, going back to the beginning again and again:
A crow flew to a stone which looked like a piece of liver, thinking perhaps it had found something good to eat. But when the crow discovered that it was a stone and not a piece of liver, it flew away to seek food elsewhere.
Like the crow that left the stone, so do we abandon Siddhartha Gautama, the ascetic, because we have lost our appreciation of his simplicity." - Chapter 3, The Stone
The stone represents the ascetic embrace of simplicity in life (and the rejection of life's distractions). Here is Charles' experience as he falls from a tall building:
"I was falling. And the stone, loosened by my hand was falling too. We fell together and the stone, near my face, was the only thing in focus. Somehow it made sense that the world would be a blur other than the stone, the stone that looked like a piece of liver." - Chapter 14, The Stone
It is not easy to get distracted when you are about to fall headfirst into the ground.