Composite Hierarchies are cosmological setting found in high end fiction, where the overarching setting is detailed in "layers, realms, planes, domains, etc.".
Within such a cosmology, the difference between these layers/planes is actually greater than the difference between physical dimensions, due to each layer containing several dimensions within them. Otherwise, these can be known as metaphysical layers.
For example: In Umineko, there's at least 5 dimensions added to each higher layer in the lowest domain (+1 temporality). Meaning the difference between these layers is qualitatively greater than the difference between dimensions.
In most cases, these meta-layers have a reality-fiction difference, meaning, the difference between each layer (not the dimensions of the layer) is like the difference between reality and fiction. Basically, to a higher layer entity, the lower entity is so insignificant that it can hardly be called real.
Not all composite hierarchies have a reality-fiction difference, and lack of a such difference does not disqualify a cosmology from being classified as composite.
Also, a composite hierarchy still fits into the Tiering System, whereas each individual cosmology should be reviewed on a case-by-case basis and tiered accordingly.