Maybe a better question is to ask whether or not it is worth it...
So how much time does the other parent spend with the child? What are the circumstances around that...? So if the other parent only sees the child every 3-4 weeks by their own choice, then you have a better chance. If, however, the other parent only sees the child every few weeks because you won't let them have more, well that ain't a good look.
If the other parent sees the kid for 4-5 nights a fortnight then you might want to ask yourself whether or not it is worth the effort... No one here can tell you whether or not you're gonna be successful. But the circumstances around the child's relationship with the other parent is going to be a significant factor in your chance of succeeding.