Can people get admission in IIM A if they retake the CAT while studying at a lower ranked IIM/FMS/XLRI?

You can surely get an admission into IIMA if you retake the CAT while studying at some other management college. 

But I would suggest you to not retake the CAT exam. You’ve gotten this seat based on your entrance rank, and other important parameters. Moreover, even if you qualify for IIMA, you would have completed a year at your present management institute. 

Though IIMA is the most prestigious management institute in India with top notch placements, your future will be defined more by your hard work than anything else. Even the new IIMs or colleges like FMS/XLRI will enhance your personality to a great extent.

Despite taking in students with a lesser percentile, the new IIMs are in no way inferior B-schools. So instead of wasting your money and time by running after IIM Ahmedabad, work on your personality and knowledge to pave your way for a bright future.

Yes, many of my friends have enrolled at IIM L after completing a year at one of the new IIMs. Your only requirement is a strong profile, a high CAT score, and a compelling reason for quitting your current business school. 

However, the opportunity cost should be considered while making this decision. This option is only practical if you come from the second generation of a new IIM or a 3 tier B-school. But you should not leave FMS or XLRI for IIM A after studying for a year in these universities. Since the opportunity cost would be too great in this circumstance.

Never consider leaving because the two years you spend there will change your perception. Newly established IIMs may, without a doubt, admit students with a lower percentile. But this is not an indication of inferior quality.