I got my start with FileMaker Pro (ver3) with an application we had bought. We received updates at least twice a year. The update renamed the existing copy to OLD. The new copy imported all data. I am just not sure how he did it. But it worked great, smoothly. And version 3 was multi-file/table at that time.
No matter how you set it up, an update will likely require an import records script that imports all data from the original copy into the new. The same script can also update "next serial value" values.
It's possible to set up a script such that an Open File Dialog opens up when the script in the new copy is run, you select the original copy of the file and the script does the import to pull all records from all tables into the new file.
And you can use FileMaker to rename a file by inserting it into a container field and then exporting it with a new name specified.
You can also design using the Convert to Seperation Model as a way to reduce the amount of importing needed when you release a new version of your solution.