Yes, it is very possible. You just need to ensure that your doctor, your nurses, and your birthing partner understand your desires, and what you want, so they can help advocate for you.
I delivered my 4th in a hospital. The only reason it wouldn't be considered "natural" is b/c I had an IV. I had a choice and I decided to get it, in case something were to go wrong, then they could quickly take care of the situation.
I had a natural labor
and enjoyed it!!