Words having two prefixes incorporated

Question

There are prefixes of time and order (pre-, post-), of location (sub-, super-), for expressing the reversing of an action (de-, dis-), and go on.

English words may take prefixes from one or two of those groups. Words of the latter types are, for example, unpremeditated or antidisestablishment.

Is there a name for words, like unpremeditated or antidisestablishment, having two prefixes incorporated?

Answer 1

After some digging, I think there is a term that can satisfy all the varied thoughts and criticism thus far. A word having two (or more) prefixes incorporated is an:

Augmentation

Augmentation is modification of a word by any of the language's related forms (prefixing, suffixing, etc).

The OED has this definition for an Augmentitive, adj. and n.:

2.b. Grammar. Of a word: augmenting the properties of the term whence it is derived, or generally expressing augmentation of an idea. (Augmentative words are generally formed by the addition of augmentative affixes.)

Emphasis mine.

This solidly establishes that Augmentation is a modification that can involve two or more modifiers, including Prefixes.

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We can see the concept of augmentation being used in the grammatical context of prefixing, while also being distinguished from (and I would say not limited to) a prefix. This reinforces the OED's definition.

1. 1646 Sir T. Browne Pseudodoxia epidemica iii. xxiv. 170. The Greek word Bous, which is a prefixe of augmentation to many words in that language.

This establishes that "a prefixe" (a single one) is a kind of augmentation.

2. 1671 E. Phillips New World of Words (new ed.). The Syllabical Augment, is an augmentation which is made in Greek verbs, by prefixing ἐ (and thereby adding one syllable).

This establishes that a syllabical augment is a kind of augmentation.

This use of Augmentation also follows the general usage of the word, which is not limited to a single [dimension] of modification. Cf. those in Heraldry and Pharmacology.

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I originally said that, No, there is no specific term for this kind of word prefixing. I think that some may still find route to argue that position. If we need a term, I don't see us doing better than this.

Answer 2

Is there a name for words, like unpremeditated or antidisestablishment, having two prefixes incorporated?

This question might have been much simpler had not grammarians long ago abducted the traditional Latin term for "prefix", praepositiō, and used it for another purpose.Wiktionary. "Prefix" is not easy to manipulate. "Position" might have been easier.
30 years ago I would not have imagined that the word agglutinated might serve a purpose in English Language matters, but, it seems it can.
There are examples of the terms *agglutinating, agglutinated, *etc, used in a grammatical sense in English today.

"Agglutination at the morphological level represents a mechanical adding of one or more affixal morphemes in pre-position, post-position or in interposition to the root morpheme. Somewhat different, however, is the quantitative representation of the parts of speech that are formed in the contrasted languages by means of preposed agglutinating morphemes." Studiopediya

" Synthetic verbs are single phonological words, formed by agglutinating prefixes and suffixes to roots of a handful of verbs, most of them intransitive".prosody.beckman.illinois.edu

Some uses apply directly to English

"One section of the book, "Vice Verses," consists entirely of slightly naughty poems involving words that have been stripped of agglutinated prefixes." Good For You

Of course, none of this creates a term for a double prefixed word. Gone with "preposition" for "prefix" are possibilities not likely to be available with "prefix". Among them might have been "anteprepositioned" "preprepostioned", "diploprepositions", etc.

Given that no term for a two prefixed word seems forthcoming, at least with any credibility, agglutinated may fill the bill as well as any word.

agglutinate; Intransitive Verb
1): To united or combine into a group or mass

2): To form words by agglutination Merriam Webster online

Agglutination

1. The act or process of agglutinating; adhesion of distinct parts.
2. A clumped mass of material formed by agglutination. Also called agglutinate.
3. Biology The clumping together of cells or particles, especially bacteria or red blood cells, usually in the presence of a specific antibody or other substance.
4. Linguistics The formation of words from morphemes that retain their original forms and meanings with little change during the combination process. The Free Dictionary.com

I would feel reasonably correct, if not precise, in using agglutinated to at least partially describe a two prefixed word.