The BBC has shown me very little respect

Larry Zweir, at Cambridge Grammar and Beyond (abridged and reformatted), classes

1. a lot of
2. a great deal of
3. a large amount of
4. quite a few
5. a little bit of
6. a small number of
7. a small amount of

as compound quantifiers.

All except (1) here can obviously have an intensifier / downtoner removed to leave a more basic compound quantifier. (This makes significant differences in all but (2).)

So 'very little', though no noun seems involved, can arguably be classed as a compound quantifier (with the simple quantifier 'little'), and hence a determiner.

Obviously, some will prefer to separate parts here, and talk about 'quantifier modifiers' by whatever name they prefer.