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I don’t see why you couldn’t purchase a health insurance policy from each employee if you’re offered a plan by each, but why would you want to pay for redundant coverage?
One plan won’t cover the other’s deductibles or co-payments, so I believe it’s better to research both plans and find out which fits your financial and medical needs and choose just that one.
Having two policies could also be a nightmare for the coordination of benefits. It’s possible that each health insurance provider might say that the other plan is primary. Just for the potential red tape alone I wouldn’t recommend having health insurance plans with both employers.