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This habit of refering to the second and proceeding beers as "another beer" may have to do with the way drinks are totted up. Typically, at least in the cafés that I went to in Seville, this involves paying not as you drink but when you're ready to leave.
Some barkeeps will calculate the "tab" in chalkmarks atop the counter in front of you. Some will keep the record on paper. Some will keep track in their heads. Some will just ask you how many beers you had.
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Return to "normal to ask for 'another beer'" ...