Hello,

If you mean whether or not you can participate in more than one state counsellings, then yes you can. You can in-fact appear for as many state counsellings or all if you want to. There is no limit on the number of counsellings you can apply for. Especially, since all candidates from around India can participate in counselling for all private colleges in India irrespective of where they are stationed (except for slightly different rules in a couple of states). 

Now in case you are asking if  you can claim 'state quota' seats in government medical/dental colleges in more than one states, then for that also, its a Yes. You definitely can claim state quota seats in multiple states, provided you fulfill the eligibility criteria (pertaining to domicile, etc.).

I hope this would help you. For further queries please feel free to write me down in the comment box.