Is there anyway to change my first round counselling alloted college and go for further counsellings?

Yes, you can write an application for that. You can also contact the college stating directly that you are not satisfied with what you got in the first round and want to go in for the second round. If you have already payed the fees, confirm that they will transfer you or refund the fees. If you withdraw your admission, the seats may get filled and if you don't get the branch or college of your choice, it can get difficult for you. be careful while making a decison and make sure you analyse alkl the pros and cons and get all the details before you shift to another college.