Is it really possible to stay friends with an ex?

Ok here’s the deal. My current guy I am seeing knows my ex boyfriend (that is a whole other topic!). Anyhow, I have always been friends with my ex’s..or have at least tried. I am currently being patient and keeping in contact with this recent ex because he was extremely important to me (I broke up with him), and I feel that with time we could be good friends again (and he also would like that). My flame maintains he doesn’t speak to his ex’s, and doesn’t want to. He thinks that is the only way for people to really “move on”. Note, he is not in any way trying to get me to stop talking to my ex…but is merely pointing out his perspective. This leaves me asking…what do you all think? Can you really be friends with an ex, and is it a good idea?