Unemployment Insurance and Freelance work

I live in NY and am about to start receiving unemployment benefits. Someone has asked me if I could do some freelance work for a couple of weeks that should give me a few thousand dollars. Is it possible to just not be paid for those weeks (say that I worked more than 4 days/made above $450) and resume the unemployment? I would rather not have to stop and start the benefits because I don't trust the company I departed from. I have never received unemployment benefits so I don't know if stopping and starting is an issue anyway. I just don't want to do something that would cost me benefits.

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