Can I have two health or dental insurances at the same time?

I've had dental insurance on COBRA from my previous job and have been paying the monthly premiums. However, the insurance just went into effect at my new company, as well. I wouldn't mind keeping both because each provides a certain maximum per year for services. Is there any reason I can't just keep... show more I've had dental insurance on COBRA from my previous job and have been paying the monthly premiums. However, the insurance just went into effect at my new company, as well.

I wouldn't mind keeping both because each provides a certain maximum per year for services. Is there any reason I can't just keep making the COBRA payment up to the time limit and keep both insurances?
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