Nope! Admission to the 2nd year of UG isn't allowed by any of the universities such as Calcutta University, Kalyani University, West Bengal State University, Presidency University, Jadavpur University etc. Now if you want have take admission in the 1st year in a  college of an affiliating university such as calcutta University, kalyani university etc. Now if you want to change your college, then you can take admission to any of the other colleges under the same affiliating university. But admission directly to the 2nd year in BA Hons. isn't possible.

For more information regarding BA as a career visit the link below:

https://www.careers360.com/courses/b-a-hons-bachelor-of-arts-honors

I hope this helps. Wish you a great day!