I am working in UK on Tier 2 (General) work permit. However, my employer has asked me to go to Switzerland for an assignment (for 2-3 months, may be multiple times in the year). He would be initiating a Swiss Work Permit. After the assignment ends, I am required to come back to UK. Note that during this assignment, I would still be an employee of the UK based company.
1. I was wondering what is the impact of getting a Swiss work permit will have on my current UK work permit.
2. Will the UK work permit be still valid if I get a Swiss work permit?
3. Can I have work permits of two nations at the same time?
I will appreciate a response. Many thanks for reading the question.

-Sachin