When to quit a relationship

So I've been with my bf on and off for 3 years.We recently broke up for 3 months and I started to move on but recently he'sbeen trying to get back with me. He seems as if he's trying to change but he's cheated so many times I honestly don't know if he's being foreal or not. But here's the problem I met someone else. I'm not in love with him but I like him. I've kind of put him on the back burner because my ex seems to always want to be around me all the time. I'm no player and I don't want to hurt any feelings. But should I give my ex another chance even though it's hard for me to trust him or move on to something new. If so,how should I go about it?

I would not give him another if he has cheated many times... be his supportive friend ...

If he HONESTLY has changed, or has realized what he did was wrong, Why not give it another shot. Just keep your guard up and see how things go. If he continues to his old ways, call it quits instantly