You can't save a copy of the database if it's shared and you are connected to it via open remote.
Best thing is to connect to the server and copy yesterday's evening backup to your desktop, then play with that.
I am wondering if there is way to save as my database on my desktop, so I can play around with various scripts without messing up the main files that are linked to the company network.
If the solution is hosted, then there is not an easy way to do this. Among other reasons, allowing an easy way to do this would provide a security risk. If the file is hosted, you are probably better off asking the system admin for a copy of the file(s) you are looking for.
If this were a local file, then saving a copy or a "clone" of the file would be the easiest thing to do and your best bet. Check out your options under FILE > SAVE A COPY AS...
Anyway take care, copied file keep "linking to the company network" if it uses IP address to link.
Good tip! I tend to get off networking when I need to examine local files that may be linked to hosted files.