An arbitrarily large group of archverses within a larger archverse is known as an Archverse cohort, though the term Ultraverse is used when the archverses within it have an extremely high nested level and the term -verse cohort is generally used when said -verses within the archverse are metric -verses with designated names (e.g. universe cohort, multiverse cohort, megaverse cohort, etc.).
Archverses with a finite nested level (“index”) are often generalized to ordinal indices. This whole hierarchy of ordinal-indexed archverses is known as Soupcount. The ωth archverse is generally considered to be the “Omniverse” or “Small Omniverse”. This article will primarily focus on archverses of finite indices while the Soupcount article will focus more on infinite indices. The creatures can be found living in these verses can be found here.
The simplest version of an archverse is to consider it a finite set of smaller archverses composed of a finite amount of universes.
These finite archverses don't contain every single possible -verse within it, and the universe can be considered finite as well. There are two ways that can be viewed. The first is to consider an archverse to be a very large hypersphere that contains a finite set of lower-dimensional hyperspheres, that go all the way down to the Universe, which can have a random number of dimensions (in our case, 3, suggesting that the Universe is a glome). The second (and probably easier to picture) way is to consider an archverse to be an isolated set of smaller archverses.
However, an isolated finite set of archverses within an infinitely large archverse, is only known as an archverse cohort. With infinite archverses, there are many ways that an archverse can be defined further than "an infinite collection of the last archverse". This is because Cosmology is subjective, and how one may think an infinite collection of already infinite -verses would be different to someone else's.
Climbing the Archverse Chain
One way to define an archverse is to extend the brane multiverse postulate. A way to interpret the Multiverse is to view it as an infinite set of 4D (3 spatial, 1 temporal) universes that exist in flat spaces known as "branes" stacked on top of one another in a higher-dimensional space, creating a space with 4 spatial dimensions and 2 temporal dimensions. Think of it like stacking an infinite amount of sheets of paper. It may seem logical to continue on from there to create larger and larger archverses, so a Megaverse can be considered to be an 8D infinite set of 6D branes containing Multiverses, and so on. One archverse would pertain a higher dimensionality from the last. The dimensionality can be given with the formula S+T+2N-2, where S is the spatial dimensionality of the universes composing the archverse, T is the temporal dimensionality and N is the nested level of the archverse. Obviously, this view has to stem from a universe with a known dimensionality (4, in this case), and -verses with a lower dimensionality than said universe aren't accounted for, not to mention the fact that its definition of a multiverse differs from a multiverse in superstring, M-theory or bosonic string theory, which suggest that the multiverses' spacetime may have 10, 11, and 26 dimensions respectively, including temporal dimensions.