Can I keep Switzerland resident permit while applying GV?

I am US citizen and live in Switzerland right now with B permit (work permit). I am trying to apply Portuagual GV. According to the recent conversation with a law firm, they told me that EU does not allow holding two permits in different countries, even though Switzerland is not part of EU, but it has close relationship with EU, there might be (not every case) a chance that SEF will ask me to give up the Switerland resident permit? Has anyone experienced this situation? Thanks.

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Thank you Jeff, I should have searched more before asking questions. However, I don’t see discussions about Switzerland case as Switzerland is not EU but has very close relationship with EU. Appreciated if anyone with the similar situation can share the experience.

The basic issues and difficulties are likely very similar. Otherwise if .ch is treated as a third party country then it’s completely irrelevant.

Technically you are supposed to relinquish your Swiss residence card once you have been issued with the Portuguese TRP. Swiss isn’t a part of EU or EEA but it is a part of Schengen agreement and if you are continuing your B permit, portugal might not be a program for your case. You can look at other available options.

Thank you all, it’s very helpful.

Is that a Swiss requirement, that you can’t hold a swiss permit and another permit?