Domain
Kingdom
Phylum
(= Plant Division)
Class
Cohort
or (animal Division)
Order
Family
Tribe
Genus
Species
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 linenan methodologies are completely incompatible in any case. But anyway, here, by way of hypothetical example, is the sequence (using the example of Order)
Superorder
Grandorder
Mirorder
Order
Suborder
Infraorder
Subterorder or Parvorder
The dimmed names are those that are generally unofficial and not often used.
All of this gives a suitably largenumber of possible heirachical levels.
I dio 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.