Non-EU B-permit going part-time in original job, restrictions for new employment?

Hi everyone,

I arrived in Switzerland with my family (wife and 3 kids) in 2017 to work as a scientific collaborator in a research group at EPFL for 3 years. We live in Fribourg, and I work here (EPFL has an antennae in FR) and sometimes in Lausanne (lecturing). In these two years, my wife has started doing a PhD at EPFL as well (so she is hired as a research assistant for 4 years) and my eldest son finished his matura and just started studying at ETH last week!

Due to me having to spend some time earlier this year in my home country and due to some budget cuts affecting our group, the professor who hired me has announced that he will be reducing my contract (putting me at a percentage, likely 50%).

I would like to start looking for a part time job as soon as possible. I might eventually even need to fully transition to it, should my original contract not be extended (likely) when it is over in September 2020.

Now, as per the long title of this post, I'm a non-EU foreign national holding a B permit. My permit card simply says: "avec activité" in front, and "toute activité lucrative est autorisé" in the back. It was issued by Fribourg.

Can anyone provide some advise for my case? Should I approach potential employers with any specific requirements?

By the way, I'm a senior architect (+20 years of experience), and PhD in Civil Engineering, and before landing here I was assistant professor at the Engineering school of a major Latin American university (just in case someone knows someone...

All the best,

Ricardo