It’s often the case that an MBA applicant can’t request a recommendation
from his immediate supervisor because it might jeopardize the job. I suggest doing exactly what you mention, asking other associates who are senior to you. And, in an optional essay, explain the situation succinctly, and why you chose the particular people.
Adcoms encounter this situation often and are not deterred by it, they just need to understand it.
Senior Advisor, Accepted
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