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I am a talented software engineer student with background in finance. I have been offered several positions at company X with different independent teams and I have also been equally successful interviewing at dozen of other companies.
I picked company X because they have a reputable business ethics in the engineering field, but with the assumption that the salary will be competitive (co-op prohibit me to discuss salaries at interviews) and that my time will be valued there, but their third party talent recruitment company later tells me that they do not negotiate on salary based on individual talents (same salary for all co-op students per level).
The salary they offered me is less than advertised on Glassdoor, and 40% less than my previous part-time position.
I know the managers at company X want my skills and see potentials in me: they ranked me first in all positions I applied after interviewing perhaps hundreds of candidates and they are having a hard time finding candidates for the positions I did not chose. They invested time and energy into securing me over dozens of other offers.
Is there a way to negotiate around a non-negotiable position from a recruitment agency?