In that situation, we would use, "もう[一本]{いっぽん}".
[助数詞]{じょすうし} can be quite confusing even to native Japanese speakers sometimes. Once the beer is poured into a glass, it becomes 「[一杯]{いっぱい}」. I would say 「[一つ]{ひとつ}」 is usually used for solid objects, but it's not applicable to all solid objects, though.
Here are links which might be helpful for you to get an idea of which [助数詞]{じょすうし} should be used in a certain situation: http://kyoan.u-biq.org/ho34-2.html and http://nihonshock.com/2012/04/how-to-use-japanese-counters/
Hope this helps :)
EDIT: The use of 「もう[一つ]{ひとつ}」 in your example situation is not grammatically wrong if the [一つ]{ひとつ} is replaced by [一本]{いっぽん}. Saying 「もう[一本]{いっぽん}いる?」 in the same situation sounds just as natural to Japanese native speakers. But these are very casual/informal, which are completely fine to use to ask your close friend. One way to ask the same question formally (one among many other possible options) would be: 「もう一本いりますか?」