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Phrase(s): (Could I) buy you a drink?
1. Lit. Could I purchase a drink for you? (An offer by one person—usually in a bar—to buy a drink for another. Then the two will drink together. Also used with can or may in place of could.) • When Sally and Mary met at the agreed time in the hotel bar, Sally said to Mary, "Could I buy you a drink?" 2. Fig. Could I make you a drink? (A slightly humorous way of offering to prepare and serve someone a drink, as in one’s home. Also used with can or may in place of could.) • Bill: Come in, Fred. Can I buy you a drink? I’ve got wine and beer. Fred: Great. A beer would be fine, thanks.
McGrawhill's American Idioms And Phrasal Verbs