What is a group of determiners called?

Question

Verbs, auxiliaries and modals constitute the verb group (Vgp).

Is there an official term used to describe a [group of determiners] (pre-, central-, post-) that pre-modify the noun in the NP? In the following examples, more than one determiner pre-modifies the noun.

[My three] cats [Both the] cats [All the many] cats

We can't call it a determiner phrase because according to the DP-hypothesis, the determiner phrase is an alternative to the NP whereby the determiner heads the whole phrase; hence, DP. This is a whole different topic.

Can it, therefore, be called a determiner group or is there an actual term for it?

Answer 1

A somewhat more useful way is to do what snailboat suggests above,
namely ignore the DP Hypothesis, which is after all just a hypothesis that can't be disproved,
and go for something that represents the data rather than the theory.

For instance, McCawley 1998 distinguishes between two types of nouny constituent in English:

1. Nʹ (pronounced "N-Bar" -- don't ask), which is a phrasal unit headed by an N
   and
2. NP (pronounced "N-P"), which is the syntactic constituent type
   corresponding to the logical type Argument of Predicate
   (and thus is outside the X-Bar nodal system).

For instance, it's not clear that the subject of

• That he arrived late is very unfortunate.
  (i.e, the complement clause that he arrived late,
  which must be a noun phrase since it's the subject),

can be said even to have a head, and if so, it's clearly not headed by a noun.
It's simply an NP, since it corresponds to an argument of the predicate adjective unfortunate.

The constituent containing determiners that precedes prenominal adjectives
is then simply, in X-Bar terminology, a Dʹ. In general, an NP will contain a Dʹ.
For instance, the subject of the following sentence

• Quite a few of the more than ten thousand people took his advice.

would be parsable as [NP [Dʹ Quite ... thousand Dʹ] [N people N] NP].

Whether Dʹ is actually the same constituent type as DP
depends entirely on one's preferred nomenclatural presuppositions.
It doesn't bear on descriptions of phenomena, except to counsel one
to avoid confusing modes of expression; after all, the idea is to be clear.

Answer 2

The simple answer to the question is NO, there is no established term such as determiner group used to denote the word combinations in the question, and there is a reason why no term has been established to denote such word combinations. This reason is that the relevant words (e.g. my three, both the, all the many) hardly qualify as a unit of syntax. At most, one can acknowledge that they form a string.

Such word combinations qualify as a constituent in no theory of syntax (that I am aware of), not in phrase structure grammars and not in dependency grammars. Furthermore, such word combinations do not qaulify as chains, that is, they do not qualify as catenae: https://en.wikipedia.org/wiki/Catena_%28linguistics%29. In contrast, verb predicates (e.g. will have fixed, has been fixed, may have been being fixed) do qualify as chains of words, as catenae. The fact that determiner strings qualify neither as constituents nor as catenae means that it is more difficult to denote such combinations with a particular syntactic term. Theoretical syntax tends to focus on word combinations that are recognizable units.

But there is nothing to stop one from establishing a new term, e.g. determiner string or determiner group. In fact, since there is no pre-established term for such combinations, one has more freedom to call them whatever one wants.