Additional insurance is optional. Health insurance companies are not required to insure you. They may exclude certain illnesses (reservations) or even refuse your request (eg due to advanced age).
In the event of an increase in premiums, you can cancel the additional insurance policies concerned within 25 to 30 days of the announcement of the increase. Some sickness funds even accept termination until the end of the insurance period (end of the year). Without premium increases, the notice period is usually 3 months for the end of a calendar year, unless you have agreed on a fixed contractual term (eg 3 years).
Whenever the health insurance fund has to provide supplementary insurance benefits, you can cancel this supplementary insurance within 14 days of payment of the benefits. However, you must continue to pay the premiums until the end of the insurance period (usually the end of the year). If you cancel a multi-year contract after one year or more, you must pay the premiums until the contract expires only.
Tip: wait until you have received written confirmation of your affiliation to a new health insurance fund before canceling your supplementary insurance. Otherwise, you risk losing the coverage you previously enjoyed!
Note: the increase in premiums may also be due to the transition to a new age category. In this case, the rules without a general increase in premiums apply. If in doubt, check with your health insurance fund!