"Make me a case" would actually be the correct phrasing. For the common lament about the "case in room eight" overlooks the central function that "making a case" has in medical thinking and action. Thus, at the bedside the individual illness is integrated into the canon of clinical knowledge ("a case of"), while at the same time the general principles of clinical knowledge (clinical picture, guidelines, etc.) are translated into singular statements and decisions for action related to the specific treatment situation at hand. Today students learn - keyword problem-oriented learning - through cases, or are examined on one in their exams.
In the field as well - that is, in court, in medical administration, or in civil society work - "case-making" relates the particular (of the crime, the problem, or the place) to general laws, rules, or patterns of behavior, and in this way enables decisions for action.