Being right that the Head, Eye, and Claw are actually separate corporations working together being A, B, and C corps respectively. At the time I never gave a reason why I suspected this and I suppose now is a good time.
Throughout LC for some reason you see terms like the Head, Eye, and Claw being used many time, but they were used rather odd. More specifically they were used like they were separate groups rather than being under a single organization. For example in the White Ordeal when the Claw appears this text shows: "To know and manipulate all the secrets of the world; that is the privilege of the Head, the Eye, and the Claws. It is their honor and absolute power."
Why emphasize the Eye and Claw? Why not just say the Head and leave it like that since the Eye and Claw are suppose to be part of the Head? Aren't the Claw and Eye just agents of the Head? I noticed this throughout LC, but decided it was just PM's way of writing and such. Later on in Ruina you see corporations working together in secret with their Singularities. Not simply working together, but dependent on each other. For W Corp alone they work with L, T, and R Corp to keep their Singularity running properly and same with the others. Each of them uses their services to prop each other up and losing even one of them it falls apart badly.
Now there is the story of the 3 birds of the Black Forest where they cooperate with each other in an effort to protect the forest. Notice how they each seem to fulfill the role of the Head, Eye and Claw? PM also confirmed that Apocalypse Bird is loosely based off them as well.
Later on we learn the Head is also known as A Corp, which was rather interesting. It's technically one of the many corporations in the City even though they are in charge. Then we learn that B Corp helps the Head in enforcing the rules they create and has regulations in place for shutting down a Wing. >Cont