MBA Entrance Exam

No, as per the college policy, you cannot.

You are clear about your professional goal. You are advised to appear for CAT in final year of BMS. Why do you want to waste one year by appearing in CAT after BMS. It will be good idea to start your CAT preparations now.
All the best.

While doing your UG you can start preparing for CAT & other exams. You can solve aptitude questions, prepare for vocabulary, read more and more newspapers, improve your communication skills & interview skills, learn how to appear in gd.
Make time table and divide the preparation for each section of paper.
Good Luck.

CAT is held every year around the month of November. It contains 3 sections namely, quantitative aptitude, data interpretation/ logical reasoning and vocabulary part. You need to clear different overall cutoff and sectional cutoffs for different business schools. It is a relative exam which means that your performance is judged in comparison to the performance of other candidates.

https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.sulekha.com/cat-coaching/pune&ved=0ahUKEwi5iaOVlrbUAhVKM48KHXigAagQFghvMAM&usg=AFQjCNHkVGFaYeZ-weD2sO4d0jlUUjleAg&sig2=MA1duS6bDN3N4kj50xC9bA
Enroll for CAT coaching classes in Pune. Find common admission test preparation courses for learning data interpretation.

Following are the good B schools where you may think about with 724 MAT composite score:
TA Pai Institute of Management, Manipal approx 700
Institute of Public Enterprise Hyderabad, 650
Balaji Institute of Modern Management Pune
ITM Khargar Navi Mumbai
Xavier's Institute of Management and Entrepreneurship Bangalore