I'm not 100% sure. I know there are group insurance plans (typically from employers) who will cover stuff like dental, vision, drugs either in part or fully up to a certain amount. You pay the difference.

Note: as far as I know, most of those private insurance plans do NOT cover your visits at the private sector. If I go pay to see a private doctor, it's like going for a massage without a doctor's note, they will refuse to reimburse.