Linux is a kernel which is often bundled with proprietary components. Android, for example uses the Linux kernel. The whole desktop operating system you seem to be thinking of is a Linux distribution.
There have been many Linux distributions with proprietary components over the years. SUSE’s YaST configuration tool used to be proprietary, for example. There’s probably something current along the same lines, but there’s not much demand for semi-proprietary desktop Linux.
What they probably can do is issue an update that lets owners point it at third-party servers, and publish the API. They might even be able to publish the source code, though there’s a chance they don’t own all of it.