In Switzerland, as an example of how it could be done (and I am a fervent and total believer in the NHS) - health insurance is compulsory- but provided by a vast number of private companies, with different rates.
They cannot refuse anyone for health reasons, disability, pre-existing conditions, etc- for basic insurance- which covers all health care. People can choose to pay for supplementary insurance for private room, choosing your own surgeon and hospital, etc. Insurance premiums vary- and each offer you a different price depending on the 'franchise' you choose- eg the first bit you have to pay yourself- and you can change that on yearly basis. So a young person in perfect health will choose a smaller premium, but a higher franchise (eg they would have to pay the first 200 per year, or 300- or 2000)- wherease someone with health problems may choose a higher premium but a very low franchise. Then everyone has to pay 10 % of claims per year- up to a certain level.
If people cannot afford health insurance, it will be subsidised by the State or even totally paid for.
It is not like Bupa, Spire or Nuffield- who pick and choose what they will or will not cover- eg pick the low risks and leave the rest to the NHS- then fall back on NHS if things go wrong
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