I suggest you 'engage' the services of a lawyer. [=I suggest you hire a lawyer]
She 'engaged' him 'in' conversation. [=she started a conversation with him]
The book fails to 'engage with' the problems of our time.
(..) What makes you think she wouldn't have sex with me? I'm a male and she's a female. Yes,but not of the same species. I'm not going to engage in hypotheticals here. I'm just trying to be a good neighbor. Oh,of course. That's not to say that if a carnal relationship (..)2007 TvShow: The Big Bang Theory Title: Pilot Season: 1 Episode 1