When given an input of some kind - physical, metaphysical, conceptual, or otherwise - the perceptible set of a Prism Gate's contents adjusts, based on whatever fundamentals it can divide the input into. It then outputs a pathway to each alternate instance of the input where each fundamental is a special case. In this way, Prism Gates generalize over any applicable property and provide access to alternate realities, philosophies, and systems.
One of the simplest uses of a Prism Gate is to give it information about a -verse (e.g. a universe) and have it output the -verse's corresponding power set (a multiverse). It accomplishes this by dissecting a universe into fundamental constants and initial values, and then listing off all relevant cases of them. Given further instruction, it will repeat the operation indefinitely, ultimately assembling the omniverse from the principles its smallest components are built on.
Cosmological hierarchies, as they are also built on orderings and permutations, are also easy enough for Prism Gates to expand on. Given enough information to define a cosmology, a Prism Gate will derive the full set of altarcae, possessing all cosmological hierarchies and concepts, all at once.
The distinctions between ultimata do not restrict a Prism Gate in any meaningful sense. Given the concept of the Box (which is either a rather small amount of information, or an inexpressibly large amount), a Prism Gate will return pathways to express all equivalent structures; everything from the Omniumverse to the Imaginarium, as expressed by the Law of Box Equivalency, is included in the results as simply alternate interpretations of the input. It is worth noting that no Prism Gate output can actually exceed these; outputs still count, in a roundabout sense, as "things" to be sorted into the ultimata once again.
With a definition of omnipotence, a Prism Gate can return all omnipotent entities; with some hierarchy or system of power, it outputs all systems that are derived from the same axioms.
A Prism Gate can work with even less specification from its input. Given no information, a Prism Gate will first derive different means of expressing information (or any other equivalent concepts), and from there construct possible logical axioms and organizational schema. The results are, of course, inexpressible, as aspects of them inevitably violate any external systematic approach to organizing them.
A Prism Gate can also operate on itself. In doing so, it produces alternate Prism Gates operating on different conceptual backgrounds, each of which will then begin assembling arbitrary axioms and information from there.
The process can be run recursively, generating an infinite loop of Prism Gates processing increasingly abstract Prism Gates and their relevant bases, though at a certain point this is no longer cosmologically meaningful and can be surpassed by a more powerful operation.