Wiktionary
keep company
vb. 1 (context transitive intransitive idiomatic dated euphemism English) To court. 2 (context intransitive idiomatic English) To socialise.
WordNet
Usage examples of "keep company".
Timothy Harris, and other publicans of good taste, lament, as the severest lot annexed to their calling, namely, that of being obliged to keep company with their guests.
Both vessels were able to keep company, but each tack took longer, each mile gained could be quadrupled by the distance sailed to achieve it.