set cap for

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set (one's) cap for (someone)

dated To try to attract, secure, or win someone as a romantic partner or spouse. (Said especially (though not exclusively) of a woman in pursuit of a bachelor.) Well, if he insists on remaining so inhospitable, then I shall simply set my cap for a man with a greater sense of charm and decency. The ladies of this town shall all be setting their caps for Mr. Rutherford, now that his inheritance has left him quite wealthy. Don't you find it rather unseemly for a man of his age and station to set his cap for a girl who's barely of voting age?
See also: cap, set

set (one's) cap for

To attempt to attract and win as a mate.
See also: cap, set