Hello,
Yes, you can take part in 2nd round counselling if you don't take admission in college allotted to you in first round. Even if you dont get a better college after round two, you can take admission in this college later also.
Infact this is why second round of counselling is conducted.
For mote counselling related queries follow the link;
https://www.google.com/amp/s/medicine.careers360.com/articles/neet-counselling/amp
Good luck

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