I've heard about this. It's called Hilbert space, and it's infinite-dimensional.
The idea is that our universe is curved into a hypersphere, which is one of many floating in 4-D space, and that is curved into the hyperhypersurface of a hyperhypersphere, which is one of many in 5-D space, and so on and on and on...
I've pondered this model myself, and it appears that everything in it is a surface. Pardon the concrete thinking, but it seems the surfaces of objects we are familiar with need a bulk to define them. Following this Chain of Being upward, we never reach the bulk until we reach infinite dimensionality, which sounds like saying we never reach it. I call this the Problem of the Fugitive Bulk. But if you're like me, you are visualizing smooth
hypersurfaces, except for tiny wrinkles that represent higher-dimensional matter and energy analogues. Maybe this smoothness doesn't happen by accident, and needs a definite smoothing process, perhaps some higher-dimensional Hawking radiation process to rapidly and selectively evaporate the little kinks that would otherwise make the structure a fractal. Anything too big to evaporate grows by accretion until its surface forms the next lower multiverse. If the big objects form catastrophically, like black holes, the formation event would look like an inflationary era of the big bang to creatures with astronomical proclivities that evolve within the surface.
Here's my solution to the bulk problem: above some critical point in the Chain of Being the smoothing process stops working, which stops the chain. Above that there is Hilbert space, the bulk, the content of which is a fractal. If this fractal is changing randomly, there might originally have been a diffusion of fractal dimension down to the threshold for smoothing, which would have triggered the evolution of nested multiverses in tiny subsets of the fractal.