keep company
keep company {v. phr.}
1. To stay or go along with (someone) so that he will not be lonely to visit with (someone).
John kept Andy company while his parents went to the movies.
I'll go shopping with you just to keep you company.
2. To go places together as a couple; date just one person.
After keeping company for one year, Mary and John decided to marry.
Who is Bill keeping company with now?
Compare: GO STEADY.
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Source: A Dictionary of American Idioms