What should I do if the man I am involved with wants to date multiple women?

My ex and I were together for a year. I had admitted to cheating, lying, and stealing from him. He forgave me but broke up with because he couldn't trust me. We still see each other all the time and are intimately involved. We still do everything like we are in a relationship but we are not dating. We still are in love but he said he has this void in his life and he needs to see other women to make him happy. I am an extremely jealous person and I have a had time with this but I want nothing more than to be with him. We have recently come to a point in our relationship where we are unhappy with each other but for some reason we can't let go. I'm not sure if I should just leave him and cut off all ties and wish him good luck or if I should stick around to show him I really do care and nothing can come between us. I'm trying to do the least selfish thing for him to show my true love and devotion but I am torn.