Providing you have a basic Swiss cover I don’t see any reason why you can’t also have a foreign policy as well. However, you may find complications if you have to go to hospital as both insurers would have to pay part of the bill.
While Swiss supplementary cover may seem more expensive there is one very big difference. Once you have Swiss supplementary cover the insurer cannot increase your premium or refuse renewal no matter how ill you become.
I don’t think you will find that a foreign policy will provide this. I suggest that you contact our resident expert
Jenny and consult her.