Voisinko saada vähän lisää kahvia?

English Translation

Could I have some more coffee?

‘Vähän’ means ‘a little’, not ‘some’.

I would say “a little” and “some” are practically equivalent. Technically, I think you could leave out vähän, as the partitive case already implies some, but it makes the request more polite.

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And I prefer ‘a little’ precisely because I think it is more polite than ‘some’. But yeah, it is a subtle nuance.