we say "another" in Korean "다른 da reun"
There are two meaning. you are fully understand "another" meaning as "다른" on your comment.
and there is one more thing meaning. "더 or 또 you can say du or ddo" in Korean
an additional thing or person of the same type as one that already exists.
"Would you like another drink?" = 음료수 한 잔 더 할래? For example I am drinking a bottle of beer and I almost drank all.
so a friend of mine recommend one more drink.
I am not sure it is helpful for you .
But I did my best to explain....haha thanks