How can I connect to a local NAS whilst connected to a remote VPN?
The short answer is that you cannot do this. Your VPN administrator has enabled a &quot;full tunnel,&quot; such that all traffic goes over the VPN. If your VPN administrator is willing to switch to split tunnels, it will work fine.
The longer, potentially getting you fired answer: you can use openconnect (installed via homebrew) to connect to the VPN. This will still have the full tunnel issue, but it won't continue to screw with the network routes after the initial connection - so you can forcibly enable split tunnels.
To connect, something like:
# openconnect yourvpnserver.com -u username --authgroup &quot;your group&quot; 

Then you can fix your routing table:
# sudo route change default 1.2.3.4 

where 1.2.3.4 is your normal home network default route. You will not be able to access any resources over the VPN after you do this, until you add routes for them:
# sudo route -nv add 5.6.7.8 -interface utun0

where 5.6.7.8 is the IP of the VPN resource you want to access, and utun0 is the VPN interface.
But again, risk of being fired if caught, etc, etc.