Would the following usage be considered archaic?
Were I you, I would ask her for a date.
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This is not archaic, but it is used infrequently. This combines both inversion and the subjunctive, and use of the latter has become more endangered for the younger speakers of English. Despite this, most speakers would use "if I were you" to describe the same sentiment. Inversion is apparently more endangered than the subjunctive.
Were I you, I'd stick with "if I were you".