Is anyone aware of a Swiss insurer that provides a service like BUPA international - ie you're covered for sickness in any country you happen to be in?

Our situation is slightly complicated. Our primary residence will be Switzerland but I spend significant amounts of time in 3 other countries (including the US)

BUPA have a product which is much more than travel insurance and which covers me wherever I am. It even provides US cover provided I don't spend more than 90 days a year in the US.

I've found nothing like this on Comparis.ch and don't know if such a policy would exist in Switzerland. If it does then I'm happy to take it, but otherwise it sounds like I'll be trying to persuade the Vaud authorities to accept my current BUPA policy!

Any suggestions on where I can get a Swiss-issued global health insurance policy?

And does anyone have recent experience of dealing with the Vaud authorities re BUPA?