Thank you so much for your reply. As suggested I requested the recommendation from my senior colleague at the last job itself and mentioned the reason in my application. I was able to submit everything in the deadline but after discussing with my recommenders they said they had under estimated the LOR for INSEAD and it was not the strongest one they could give, with the time constraint. (made a mistake by not sharing it with them long ago) An INSEAD alum has also recommended me directly, I wanted to know if there is a point in getting a personal recommendation from a senior industry professional (as mentioned before) which might provide a different perspective than the professional ones and how will this be possible. (Also you mentioned around interview time, did you mean once shortlisted for the interview or closer to the shortlisting date)
This is an absolutely fine plan, and I don't think this will jeopardize your candidacy in any way. However I would recommend that you mention in the additional information section that you are keeping your intentions confidential which is the reason that your supervisor is not one of your recommenders.
Make sure that everybody is telling an anecdote firsthand that shows they have observed you demonstrating leadership teamwork problem-solving and initiative.
The additional recommendation is truly additional you don't need to have three people, and it's actually a little better for you to wait until the middle of the process may be around interview time for you to bring this one forth.
It's ideal for you to have an alum of the school but I think your idea is also good. However it's also a test in judgement!
Meaning, it should only be someone who is bringing a different angle to your application supplementary to the rest of what you already have.
Don't move forward with a third recommender just to fill the space that's not going to work to your advantage.
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