Hi there,
Yes, it is possible to take out supplementary health insurance from a Swiss insurance provider without getting compulsory health insurance from the same insurance provider.
However, some insurance providers only accept applications for supplementary health insurance policies from applicants who also take out their compulsory health insurance. The requirements vary between insurance providers and also between insurance types (i.e. outpatient insurance, hospital insurance).
If you are interested in a supplementary health insurance policy, a good first step is to contact the insurance provider and explain your situation. Only apply once you have the confirmation that you can get the requested policy, so as to avoid having your application rejected.
Best regards from Moneyguru
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Swiss hospital insurance comparison