Superplural

The singular number, I understand, denotes one, and the plural more than one, but to describe the number of flies we have here would require a super-plural. It is not that we have merely 'more than one'—we have myriads of flies.

Source: wiktionary

[§ 41, page 45] Some nouns of singular form, already producing plural reactions may be further given plural suffixes; it is convenient to call these forms "super-plurals." […] [page 454] It appears that Super-plurals do not denote a large quantity of matter in one place, but a number of lots of matter in different places, e.g. grain collected or growing on different people's holdings.

Source: wiktionary

There are, of course, no super-plural terms or quantifiers in English, but I would like to suggest the relevant semantic category is nonetheless legitimate: super-plural quantifiers are to third-order quantifiers what plural quantifiers are to second-order quantifiers.

Source: wiktionary

[Agustín] Rayo (2006) develops an alternative that allows for absolutely unrestricted quantification. It consists in using languages that contain not only plural terms, but also terms that are "superplural", "super-superplural", etc. […] A superplural term may refer to several "pluralities". […] As we will show, in order to specify the truth-conditions of sentences containing mass nouns and plurals, we will need to be able to refer to several "pluralities". We will do so using superplural terms.

Source: wiktionary