Fate/Apocrypha material - Encyclopedia: Other Side of the World [Others], p.173
[T]
Reverse Side of the World [Others] The place where the evil dragon Fafnir finally arrived at the very end of the novels. The Phantasmal Races, having understood that the Age of the Gods was over, ceded the Earth's surface to humans and moved to this place. The world where humans currently live (including the laws of physics) is like a
fabric that thinly extends across the surface of the planet.
Beneath that fabric exist the planet known as "Earth". On the other hand, the
Reverse Side of the World is the world as it was before humans lived there… that is, the fabric of the era where Phantasmal Races strode the land. In other words, the
Earth is the bottommost layer of the planet, and it is
covered by the "Reverse Side of the World"—the place where the laws of the "world" as it once was reigns, and c
overing that is the "Present World".
In the Reverse Side of the World, the Holy Grail cannot activate its function of "using the Third Sorcery". In the first place, that function was for the sake of granting Shirou Kotomine's wish. In other words, it is programmed to target humans, and doesn't count Phantasmal Races as valid targets.
Jeanne d'Arc is a Heroic Spirit who, from the start, lost her human body long ago. Because of that, the chances of her reaching the Reverse Side weren't completely zero… However, that is merely the kind of "not zero" like, as a comparison, somehow managing to pass through a wall with the tunnel effect, but the Throne where Heroic Spirits Exist is cut off from the time axis, so she effectively had an infinite number of attempts to try.
Taken from the Apocrypha source matireal its states that the reverse side between the physical planet and the Common Sense of mankind, if Layers are a sense of dimesional space as you said, and the common sense of mankind is still 3D, the by your words the the dimensions would scale by 3, 4, then 3 again. These layers are local only the the planet Earth and are more akin to Reality Marbles created by the planet as dictaded by the major influence; Phantasmal Beast for AoG and Humans for AoM.
If these Layers were full blown dimensions then they would extend past the earths and encompus the entier universe but they don't so they can't be dimension as of how we define them. And no saying they could have a different meaning then our own would defeat the purpos of calling them physical Dimension in the first place. You don't call Magic science just because it doesn't fallow our definition of Magic.