Employment Law Questions? Ask an Employment Lawyer.
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Unfortunately, the only other way around this would be that you would have to insist on any subcontractor you are using to provide their own proof of workers compensation coverage that you would then provide to your clients. Other than mandating that the subs provide their own proof of workers compensation insurance, I am afraid your only other recourse is one I am sure you are trying to avoid and that is to hire the subs on as employees of your company to provide them coverage.