|The Linnaean System|
The sequence Kingdom Phylum Class Order Family Genus Species is mandatory in the Linnaean hierarchy. Non-compulsory grades have however been added, such as the Tribe between genus and family, and more recently the Cohort between class and order, and Domain above the level of kingdom. All of which gives the following sequence:
Phylum = Plant Division)
Cohort or (animal Division)
And although the subcategories super- sub- and infra- are most widely used, new subdivisions have recently been created, such as subter- parv- magna-, grand-, and mir-, to take into account the extra subdividing due to the influence of cladism. Many of these new sub-divisions are not generally accepted, and are not likely to be, as the cladistic and Linnaean methodologies are completely incompatible in any case. But anyway, here, by way of hypothetical example, is the below sequence using Order as an example:
Subterorder or Parvorder
The dimmed names are those that are generally unofficial and not often used.
All of this gives a suitably large number of possible hierarchical levels. I do however feel that just as "tribe" was added between family and genus, and "cohort" between order and class, it would be useful to have a further optional grade between family and order.