What to do about continuing unemployment benefits and a part-time job?

Question Details: About 8 months ago, my full-time job was eliminated. I accepted a part time job with the same company, and I've been collecting partial unemployment benefits. I am considering a new part time job offer, however I do not want to lose my partial weekly unemployment check. The hours of the new job overlap with my current one, so I can't work both. If I quit my current for the new one, will I be disqualified from my current benefit? After all, my current benefit is based on the company I currently work for. If I quit to switch jobs, can my current employer protest my unemployment for voluntarily quitting?

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