In General Schemas Theory (http://emergentdesign.net) there are ten schemas stretching from -1 to 9 dimensions and the top two are Kosmos and Pluriverse. I take it that Pluriverse and Multiverse is the same thing. What is above the schemas is string theory, but as far as I know there are no schemas associated with string theory in the tenth and eleventh dimension. Schemas are a priori templates of understanding that we project onto experience. Both Kosmos and Pluriverse are idealizations that we do not actually experience, more or less projections beyond experience that just serve to give context to our world which is the furthest horizon of actual experience.
But in General Schemas Theory we observe that there can be recursive nesting of any schema. So for instance in Systems Engineering they are enamored by the idea of the System of Systems, which is really just a recursive application of the idea of System to the next level of scoping. So what they are really describing is the Super-system, and of course we can go the other way and describe sub-systems to any level of scoping we need. On this analogy it is possible to recursively apply the pluriverse schema to the pluriverse itself and so we get the super-pluriverse as the next level up from the pluriverse, and it is beyond experience also. However, I don’t know if scoping down to the sub-pluriverse, unless Lee Smolin is right and black holes are baby universes.
So there is no problem handeling any level of recursive scoping of the Pluriverse being applied to itself, and that should handle any degree necessary of multi-multi…n level-multiverses. But the real question is whether there is any schema beyond the pluriverse, and in my S1 hypothesis there is not. String theory takes over but we have no schemas for the tenth and eleventh and above dimensions. So basically we draw a blank when trying to think about any different organization above the pluriverse. I am saying we can’t really imagine it and we don’t visit such a place in our dreams, where we are schematizing like mad in a freewheeling way unconnected to sensory experience.
The most interesting dimension beyond what is schematizable is the twelfth dimension where F theory appears beyond M theory, where there are two orthogonal time lines. This leads to the idea that time is perhaps multi-dimensional which is an idea that Dunne had around the 1920s but which was not taken seriously by physicists. Dunne influenced Tolkien who represented the characters of Lord of the rings as having different experiences of time.
Thus I would call the next higher level multiverse the super-pluriverse just like there is the super-system, i.e. the pluriverse of pluriverses like the system of systems where recursion is applied upward, and of course that recursion could be infinite. But I would make the statement that there is no higher schema than the pluriverse or multiverse that is a different organizational template of spacetime. There is no macro-schema higher than the pluriverse because it cannot be imagined. But that is where string theory takes over and articulates the various ways that one dimensional monads can interact within that higher order non-schematizable timespace plenum.