L permit holder, addresses in two cantons

Hello everyone!

Hoping some of you may have input into my query, thank you in advance for your insights!

I am an L permit holder (non-EU ), currently having a primary residence address in Zurich Canton.

Here is the question-> Am I allowed to rent another flat in another canton (e.g. Zug)? While keeping my primary address/registration in Zurich.

Thank you for your leads/insights!