Hello aspirant. Yes you can apply for MBBS in private medical college of other states. They give admissions for students who are non-local and have separate quote where they intake depends on number of seats reserved for that quota. So go ahead and apply in other states. 

Good luck.

Thank you. 

Hey Aspirant !
Surely you can apply in the Private medical colleges of other states irrespective of the fact that you have the domicile of a single state.
The private medical colleges release their own counselling dates and cutoff so if you are willing to take part, then you need to select the institution and carefully go through their website to make sure about the particular dates.
The colleges will take in students only on the basis if their NEET marks.

Hope this helps.

All the Best !