I'll go get us some drinks while you two 'get better acquainted'. [=while you two talk to each other and get to know each other better]
The two actors are intimately/casually 'acquainted'. [=they know each other intimately/casually]
He 'acquainted' the new employee 'with' her duties. [=he told her about her duties]
(..) You want some coffee? Yeah. Sure. Her husband is Dr. Lawrence Bell. But back when we were acquainted, Four years ago, Do you have a towel? Yeah. Thanks. You still take cream and sugar? Yeah. (..)2003 Kill Bill: Vol. 1
(..) Put your hand on the Bible. Do you solemnly swear to tell the truth, the whole truth, so help you God? - I do. - Sit down. Were you acquainted with Mayella Violet Ewell? Yes, sir. I had to pass her place going to and from the field every day. Is there any other way to go? (..)1962 To Kill a Mockingbird
(..) - Hi. - Hi. It is so, so nice to meet you. - Hi. - Thank you for agreeing to see us. - Hi. - I'll let you get acquainted. - Okay. - So it's Monica and Chandler? I only know you as "File CRW-D." That's what our friends call us. (..)2004 TvShow: Friends Title: The One with the Birth Mother Season: 10 Episode 9