Welcome to the Forum, Ivan Ivanov!
Yes, you’re right that the words you listed in your posting above are determiners. Specifically, the following determiners are of the type known as identifiers: (1) the articles: “a,” “an,” “the”; (2) the demonstratives: “these,” “this,” “that,” and “those”; and (3) the possessives: “my,” “our,” and “your.” On the other hand, the following determiners are of the type known as quantifiers: “few,” “little,” “several,” “some,” “half,” “enough,” “many,” “much,” “either,” “every,” “each,” and “any.”
The words “both” and “all,” which are used to express an entire amount or inclusion in a set, are definitely not quantifiers. They belong to a class of words known as predeterminers. By definition, a predeterminer is a word placed before an article or determiner to give even more information about the noun that comes after. Another set of predeterminers are the words “such,” “what,” “rather,” and “quite.” They are placed before the indefinite article that precedes a noun and are meant to express surprise or intensify feeling, as in “What a beautiful day it is!”
Some grammarians go further by classifying predeterminers into the following four types:
1. Intensifiers: “rather,” “quite,” “such,” “what,” “other.” Examples: “This apartment is rather cramped for the six of you.” “Aside from being intelligent, she’s quite a beauty.”
2. Multipliers: “twice,” “thrice,” “four times,” “ten times,” etc. Example: “His condo is twice the size of mine.”
3. Fractions: “half,” “one-fourth,” “four-firths,” etc. Example: “They consumed half a year’s supply of food.”
4. Includers: “both” and “all.” Examples: “Both of his cars are under repair.” “All of his assets are gone.”
We must keep in mind though that traditionally, the above predeterminers are considered simply as adjectives like the demonstratives and possessives. It is primarily to highlight or emphasize their distinct functionalities that they are reclassified as predeterminers, then are further broken down into the four types listed above.
As to your second question, no, I don’t think we can classify as determiners these phrases that you listed: “a great amount of,” “a good deal of,” “a great deal of,” “a lot of,” “lots of,” “a good/great many,” “many a,” “a (great) number of,” and “plenty of.”
Remember that by definition, a determiner is typically a single word (like “this,” “some,” and “every”) that’s used before a noun to show which thing or thing is being talked about. Technically, the mere fact that those phrases consist of two words or more already disqualifies them from being considered as determiners; and as far as I know, there are really no such things as determiner phrases in English grammar.
I think those phrases that you listed above can be more properly called premodifying phrases, which consist of a determiner up front (or none at all), an adjective next, a quantifier next, and a preposition next, all of which precede the noun (the headword or nominal head) that they are supposed to modify. This is clearly the case with, say, the premodifying phrase “a great amount of” in the sentence “A great amount of resources has been devoted to that project, but to no avail,” where the premodifying phrase describes the headword “resources.” A variation of that premodifying phrase without a determiner up front is when the quantifier is plural, as in “Great amounts of resources have been devoted to that project, but to no avail.”
Lastly, you asked whether the following words can be classified as determiners: “the only,” “such,” “other,” and “another”; and “the same,” “the very same,” and “the next.”
I already pointed out that “the only,” “such,” “other,” and “another” are not determiners but predeterminers that fall under the intensifier category; “the same” and “the very” are likewise predeterminers under the same category. See how they work in the following sentences: “The grand prize winner is the very same guy who won it last year.” “The culprit turned out to be the very woman they thought was incapable of wrongdoing.” In both sentences, “the same” and “the very same” highlight or intensify the uniqueness of the subject being identified.
As to the phrases “the next” and “the previous,” I don’t think they should be classified as determiners at all; in both cases, in fact, only the definite article “the” is a determiner. I would consider “next” and “previous” simply as adjectives that indicate position in a physical sequence or in time; they are not predeterminers either and are definitely not in the same league as “the only,” “such,” “other,” and “another.” These last four function as intensifiers as I’ve shown earlier, but “next” and “previous” don’t do so; they only indicate relative position in an objective, dispassionate manner. Indeed, nothing is emphatic or emotional in a sentence like, say, “She was the next in line at the ATM booth” or “The previous occupant of the apartment has migrated to Canada.”
I trust that the discussion above has further clarified things for you about the nature of determiners, predeterminers, and the common run of adjectives.
