The only thing you could do is to:
‘clone’ your server,
Thereby making sure that all media files are available on the new server under the same address/path name/drive letter as they were on the old server.
https://support.plex.tv/articles/201539237-backing-up-plex-media-server-data/
I strongly recommend you to clone the server onto the same platform/operating system type.
Crossing platforms (e.g. Windows -> Linux) is only for advanced users and requires additional editing of the database.
After you have cloned your server, edit the ‘advanced server config’ of the clone
and remove the following keys:
- AnonymousMachineIdentifier
- MachineIdentifier
- ProcessedMachineIdentifier
- PlexOnlineToken
On the new server, you can afterwards delete all those libraries which should only remain on the old server.