Do buy open-backed headphones if you want your ears to breathe. I cannot wear closed headphones for more than 30 mins, while open-backed can be used all day.
You can't just take open back headphones and close them up, it will sound terrible. And conversely you can't open up a pair of closed headphones without the same problem.
If you could make a headphone that can do both and sound acceptable, it would probably much more expensive than just buying a two pairs, one open and one closed.