Hi, 

Yes you can apply for karnataka private mbbs colleges if you are not a domiciled resident of karnataka this can be done through all India quota counselling. 

You have to fill the karnataka private mbbs colleges names  in the all India quota counselling form.and you will be eligible for getting a seat there in the private college according to your marks and fees would be higher. 

If you will have any other doubt you can ask us