The SIVerse notation scheme is another way to describe -verses that's been hinted at in the wiki. I've decided to expand it into a complete classification.
A universe sits at the centre of the classification. It's just you're normal universe, being the totality of existance and all that. Basic stuff.
Large SI Prefixes
Large SI prefixes make larger universes. A kiloverse is what would otherwise be called a multiverse. A megaverse is what would otherwise be called a metaverse. So on, and so forth.
Small SI Prefixes
What about smaller SI prefixes? A solution to what these could mean can be found with the application of some intuition, and some hard numbers .
A universe can be considered as containing multiple galaxies, widely spaced. These are located at 3.0 on the Kardashev scale, one lower than that of a universe, as well. They're also the largest layer of organisation that has this property (the space between galaxy clusters, for example, is small compared to the size of the clusters themselves). Therefore, a milliverse is what we would otherwise call a galaxy.
Likewise, a galaxy is made of many widely spaced stars, which sit at 2.0 on the Kardashev scale. So, a microverse is what we would otherwise call a star, or a solar system.
A solar system is made of several planets, widely spaced, which sit at 1.0 on the Kardashev scale. So, a nanoverse is what we would otherwise call a planet.
Below this, the scale breaks down a little. Planets are, physically, dense down to the atomic level, but atoms are very far down on the Kardashev scale. By using a civilisation-centric system, however, we can make some intermediate levels by using smaller values on the Kardashev scale. A picoverse is approximately a neighbourhood (K0.1). A femtoverse is approximately a tissue (K-0.8). An attoverse is roughly a biomolecular complex (K-1.9). And a zeptoverse is about a quark (K-2.9).