Translation:I would like another cup of coffee, please!
Question: "noch" is written always with "eine"? Duo says that noch is another so I don't understand why eine is necesary.
'eine' functions like the 'an' in another, 'id like other cup of coffee' makes just as little sense as 'ich möchte noch tasse kaffee'
I think "I'd like another coffee, please" should also be accepted as it's quite obvious the coffee will be in a cup of some kind, presumably in the same cup as it was before.
I think you're almost right. Most people would read it as "...another cup", but since "noch" can also stand for "immer noch" (still) this might be said by someone who is still waiting for their first cup. But because "möchte" is "want" or "would like" it would have to be "I'd still like..." or "I still want..." and not "I still like..."
I think its because Tasse (Cup) is feminine, and this comes before Kaffee which would of been masculine.
That sounds unnatural. "I would like yet another cup of coffee" works, but implies a sense of unexpectedness that you wanted more at all.
I learned "moechten" as "would like" or "should like". My translation was, "I should like another cup of coffee please" but of course it was not accepted.