OBW starts with: "It is worthless, this old pen case I brought from Viron. It is nothing. You might go around the market all day and never find a single spirit who would trade you a fresh egg for it. Yet it holds... Enough. Yes, enough. I am sick of fancies."
I believe we can take the old pen case as a metaphor for the old body Horn has brought back from the whorl. "At present it holds two quills, for I have taken the third one out. Two were in it when I found it in the ashes of our shop. The third, with which I am writing, was dropped by Oreb not so long ago." To push the analogy, the three pens are three spirits: Silk, Pas, and Horn. The third, with which he begins to write this book, will be "dropped" before the end.
I believe we can trace the major changes in the contents of the "pen case" through key events in the book:
1) Horn falls into the pit, dies, and is resurrected after three days by the power of the Neighbors. I believe this is when he gained the power to astral-project. Many have asked why he didn't use his astral projection power to visit Nettle: in fact, he did so once and it frightened her so much that he never repeated it (OBW 9, p. 203).
He probably also gained the power to alter stories at this time. One aspect of this seems to be the ability to alter objects in his own possession. He converted the ring Oreb found into Seawrack's ring, and he converted the leather-and-metal pen case he found on the steps of Smoothbone's ruined shop (RttW 12, p. 252) into a leather-and-pasteboard pen case "found... in the ashes of our shop." (I think Horn didn't want to admit to himself that his father ran back to the old shop and left his own personal pen case for Horn to find when he excused himself at the tavern).
2) Horn hears Seawrack's siren song and becomes enthralled by it. From then on, he can hear her singing whereever he is, and even infect others with this ability (IGJ 17, pp. 266-267). I don't remember whether he can hear her on Green or in the Whorl, but he probably can't on Urth since he calls the Matachin Tower a haven of rest and prayer (RttW 13, p. 263).
3) Horn is transferred into Silk's body on the Whorl. Silk is in the middle of mourning the death of Hyacinth and has cut himself in grief (I believe that this is the traditional cutting of a mourner rather than a suicide attempt). Horn/Silk denies who he is, realizing that if he really replaced Silk he has destroyed the object of his mission. He pins his hopes on the Silver Silk in Pig, but knows he cannot take Pig to Gaon without endangering both of them.
4) There was probably a transfer and merging of Passilk into Horn/Silk as well. Note the silver monitor screen in Pig's room (RttW 18, p. 372). Once Pig had a working eye, an upload and re-download into Pig and Silk was feasible. (Note: the idea that Pig was born blind is absurd -- the Passilk possession requires that he was sighted at the time he killed the auger, not to mention that a blind man becoming a mercenary at all is nonsensical).
5) At the escape from Gaon, part of Horn's spirit is projected into Babbie. This might have been enabled by the Neighbors or the Outsider. More of Silk's personality is evident after this in the next book. Just like the hunted Scylla, this may have been intended to protect part of himself in case the inhumus killed him.
6) There is a huge change in the appearance of Silk's astral form between one visit to Urth and the next. The difference seems to be the visit to Greater Scylla. I believe that Horn's spirit separated from Silk and went into one of the undine tentacles of Scylla. Hoof sees the undine with glowing eyes who smiles at him, just as Babbie smiled (RttW 17, pp. 365-366).
On the return from this projection Babbie is sleeping, and I believe Babbie also lost his part of Horn at this time. We don't see Babbie acting human again, and he eventually returns to Witch Island and Mucor. He apparently doesn't go to the Whorl with Silk. In any case, as an animal his lifespan is limited and he might not have lived long enough to travel with the Whorl when it was ready to go.
The attraction of the Greater Scylla to Horn's spirit is probably because of his enthrallment by Seawrack. In IGJ, Horn knew that a return to Seawrack would be suicidal and he asked no better death. Silk's deal with Greater Scylla to summon the Mother and get Seawrack back was probably also suicidal in intent, but his scruples about unfaithfulness to Nettle made him decide not to do that "while Nettle was alive" (RttW 20, p. 407). Instead, he chose to provoke Juganu to kill him. But after talking to Remora and realizing that he was Silk and that Horn was gone, he knew that he could summon Seawrack safely and get her away from Blue. (He was not Nettle's husband at all now, so he could call Seawrack even though Nettle was still alive.) Getting Seawrack away from the Mother's influence might have enabled Silk to redeem her from being the siren man-trap she was into a fully human woman in time.
7) Horn in the undine may have humanized her to some extent. It may be that his influence caused this undine (separated from Scylla to become Juturna) to intervene in Severian's life in positive ways, contrary to the will of Abaia.
8) Severian's memories of the good Silk looking like the ghost of Malrubius (and also positively associated with the dog Triskele) probably influenced the character of the aquastor that the Hierodules made for him. I don't believe Silk himself revisited Severian to be that aquastor himself.