Yes, definitely one can attempt first as well as the second round of counselling. Basically there is second counselling because certain students leave their seats for they get into other good colleges or for some other reasons. So, if you haven’t got your dream college in 1st counselling then you can go for the second round. If you are lucky enough you could get your seat in your desired college.
All the best for the counselling.
Hope you get yours 🙂