Can job change be done 1-2 months before Bschool application

unc123 I would not do it unless it is very clearly advancing you in a directly that is more in alignment with your post-MBA goals. And that does not seem to be the case. It's a move up, doing the same job at a bigger company, but puts in question how much you want/need an MBA to get to the next step.

Outside of being in the startup arena, it is a bit frowned upon to leave a job in less than a year. And, you will forever have to explain that yes you switched jobs and applied to business schools at the same time. This shows you did not really change jobs in earnest; it was insincere.

This is a bad look on you and makes you appear to be a risky investment from the perspective of a future employer. The story will be on your CV forever. I think it would do more harm than good.

Also, its far better to work with recommenders who have known you for a while. Who knows how your future job will go - if you leave your job now a) will your manager still be as excited to help you in your recommendations and b) you will not be able to ask your new manager given that you just got there. Recommendations are very important - schools want the scoop on you from others even more than what you say yourself.