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To express a willingness, openness, or eagerness to pursue something, such as a relationship or an intended course of action. Being new to the area, I made friendly overtures to some of the parents in the toddler playgroup in the hopes of making some new friends. The senator made overtures about changing the tax code during his election campaign, but since being elected he hasn't done a single thing about it.
make overtures about doing something
to give hints about something; to present or suggest ideas. The company made overtures about hiring me. Tom is making overtures about inviting us to his country home next month.