Wiktionary
vb. 1 (&lit take up take up with English) 2 To form a close relationship with (someone). 3 To become interested in (something). 4 (context archaic English) To be contented to receive; to receive without opposition; to put up with
Usage examples of "take up with".
However, as you are so condescending to take up with the best I have, do, Susan, get a fire in the Rose this minute.
In the country, indeed, one is obliged to take up with all kind of trumpery.
Keep my eager sister waiting and she'll likely take up with some passing stray Arab.
In short, then, he remained at home fifteen days very quietly without showing any signs of a desire to take up with his former delusions, and during this time he held lively discussions with his two gossips, the curate and the barber, on the point he maintained, that knights-errant were what the world stood most in need of, and that in him was to be accomplished the revival of knight-errantry.
If you're convinced that this kid she wants to take up with is no good, then why don't you help her to see it?