Took up with is a phrase that typically means someone began associating or forming a relationship with someone or something. The antonyms for took up with could include separated, distanced, and disassociated. To be more specific, separated implies a complete removal from someone or something. Meanwhile, distanced means staying away or creating space in one's relationship with someone. Lastly, disassociated refers to removing oneself completely from a situation, organization or relationship. These antonyms can be useful when trying to convey a message of discontinuing or ending an association with someone or something.