The Barrelplex is the "default" altarca assumed to be in play by this wiki's shared cosmological elements; it is marked by a simple recursion at the lower levels, counting upwards, via powersetting or similar operations, from universes through omniverses and the like. Other altarcae do not need to have any of these traits. Some can be closed loops, where the "largest" -verse is contained by the "smallest", while others branch off into multiple loops that are then surpassed by something else. Certain altarcae are "small" and have only a finite number of levels within; others are "large" and complex enough to surpass even the usual notions of post-infinites or the concept of meaningful arrangement itself.
Altarcae can contain themselves, larger altarca cosmologies, ultimata such as the Box or the Omniumverse, or anything else that forms a cosmology, but they are ultimately still contained within the Box. In this way, they can be compared to the imaginata of the Imaginarium, except mapped to cosmologies rather than imagined realms.
An entity or structure that is somehow not part of any cosmology can be said to exist within metempiric space, but doing so without inadvertently defining oneself as a cosmology of sorts (and thus an altarca) is difficult.
This wiki's Cosmology Tier page effectively details the contents of various altarcae.