Synonyms of 'go out with'
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He's been going out with her for six weeks now.
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If you are courting someone of the opposite sex, you spend a lot of time with them, because you are intending to get married. You can also say that a man and a woman are courting.
I was courting him at 19 and married him when I was 21.
date (informal , US)
He's been dating her for three months.
go around with
be romantically involved with
go steady with
step out with (informal)
If a man woos a woman, he spends time with her and tries to persuade her to marry him.
The penniless author successfully wooed and married Roxanne.
Thesaurus for go out with from the Collins English Thesaurus