I don't understand for which course you are asking this question. From a general sense, most of the private engineering and medical college offers admission to any students all over India if it accepts score from the All Indian entrance. For engineering there are also state level entrances, so you have to confirm first which examination you have to give in order to seek admission in other state college for this courses.

Now as per the question you have asked, I think you are asking about the private medical college (this is my assumption and if this is not your requirement, I would recommend you to repost the question with proper question specifics [name of the course for which you are asking the admission criteria in other state] so that we can provide you all the information required) as the NEET counsellings didn't started, this feels the most relevant. Now the colleges offering the admission through All India Quota, you can get by following the link below:

https://medicine.careers360.com/colleges/list-of-private-medical-colleges-in-india-accepting-neet

For NEET college predictor visit the link below:

I hope this answer helps. All the very best for your future endeavors!