If I ask how many people showed up at a party, an answer might be 'a few.' Another answer could be, 'quite a few.' The first phrase means a small number, while the latter means a comparatively large number.
It follows that the meaning of 'quite a few' is not built up from the meanings of 'quite' and 'a few.' This is so whether 'quite' is taken to mean entirely or very.
Equivalently, the meanings of 'a few' and 'quite a few' have no common meaning element. 'Quite a few' functions as a semantic unit. Its meaning cannot be arrived at by piecing together the meanings of 'quite' and 'a few.' It must be learned as the unit it is: 'quite-a-few.'
I rejoice in being a native speaker of this irregular and illogical language. Irregular and illogical as she is, she is my thought's alma mater, and I love her dearly.
But my love is not jealous. I do not begrudge the foreigner who attempts to learn my language and share in her charms and foibles.