It's definitely not impossible. I'd say some people can, and some people cannot.
There will always be things you cannot change, but as far as MBTI types go, yes. Yes, you can change.
Why? Some people stop growing in their early twenties, and that is probably closely related to when they stop developing their brains as well.
After that, it's just downhill. If you, however, continue learning on a daily basis, you don't stop growing intellectually, spiritually or even physically (as far as developing your brain).
I read some study on that. Some people, lifelong learners, does not stop growing because they keep their intellectual metabolism running.
It's just a thought, but if you think enough and don't get stuck in a rut, yes. Then you can change and continue to change.
You'll never be finished if you continue, but you'll keep getting better. Probably a little less sane, as well, though.