The phrase "they engage with" is correct and usable in written English.
You can use this phrase when you are discussing between two or more parties. For example, "The children engage with each other every day at school."
Untold social media companies have little following or engagement on the very platforms they engage with.
Also, increasingly, they engage with us emotionally.
Patients are seeking greater choice and flexibility in how they engage with self-management programmes.
There's the matter-of-fact way they engage with pop, and especially funk.
When they do have a case, they engage with the argument, he says.
And there's a subtle difference in how they engage with the audience".
"At Gucci Group, we recognize their transformative power in the way they engage with luxury brands.
"The fact they engage with us indicates we've hit a nerve," Mr. LeBaron said.
Universities need to review why they engage with the wider world before they lose their way.
To demand that people leave their faith behind when they engage with politics would be absurd.
Readers move into a different mode when they engage with a glossy.
