You can try-but very difficult.. If you want it in writing in the contract you can definitively ask, unclear how flexible the powers that be will on that. Most academic contracts are pretty boiler plate when it comes to vacation time (ie 4 weeks off). PP contracts are definitely more flexible on this. It’s also notable that at least at my institution we’re on the honor system re; vacation and personal days. so long as people don’t take advantage. I’m sure there are other institutions that are more strict.
Re; more compensation. I’ve seen asking for moving costs, signing bonus, covering board exam costs all work. Asking for a higher base is often futile but worth a try. Others things to consider, if there is any flexibility on bonus (some institutions use wRVU based bonuses ie productivity bonus) Several colleagues of mine have been successful in getting an extra 5-10k. Academic jobs don’t leave a ton of room for negotiating but like I said no harm in trying and see what you can get.
(I’m at a nyc hospital btw)