American girlfriend finishing EHL degree—any advice on staying in Switzerland?

Hi everyone, I’m Swiss and my girlfriend (a U.S. citizen) is finishing her bachelor’s degree at EHL soon. She really wants to stay in Switzerland after graduating, but she’s having a hard time finding a job that would sponsor her for a work permit.

We know it’s tough for non-EU citizens to get hired unless the job is considered “highly qualified,” and a lot of companies seem hesitant once they hear she needs a permit. She’s applying mostly in hospitality/business roles but hasn’t had much success yet.

For anyone familiar with the process:

•	Are there industries or companies in Switzerland that tend to hire non-EU graduates more easily?

•	Do recent Swiss university graduates have any special options for staying after school?

•	Any tips on how she can improve her chances or where she should be looking?

We love living here and would really appreciate any insights, experiences, or suggestions from people who’ve gone through something similar. Thanks a lot!