If you want to run two different versions of the application, all you need to change is the assembly name to make ClickOnce a different version. This makes me wonder if the assembly name of the main application will change if it still appears as ClickOnce as the same application.
If you need to change the assembly name (and I would like), you will have to uninstall and reinstall the application. You can do this programmatically for them; it only takes a minute.
The MSDN article, "Certificate Expiration When Deploying ClickOnce," when a ClickOnce certificate expires, shows how to programmatically remove a ClickOnce application and reinstall it from another URL (code is available). We have done this several times, and it works very well and is not intrusive to users.
I am sure that you cannot just create a new version for the new URL and copy the deployment manifest to the old deployment folder, because you change the application identifier and do not recognize it as an update, but you can always try.
RobinDotNet
source share