The phrase "takes up with" refers to someone associating or becoming involved with someone or something. Antonyms for this phrase could be "detaches from," "disengages from," or "separates from." These antonyms convey a sense of distance or separation rather than association or involvement. Other antonyms could include "avoids," "rejects," or "ignores," which suggest a deliberate choice not to become involved. Another useful antonym might be "disowns," which conveys a sense of actively cutting ties with someone or something that one has previously been associated with. By using these antonyms in place of "takes up with," a writer can convey different shades of meaning and nuance in their writing.