Have you added a new game, and tried using the WINE runner? Let us know what happens. Failing that, you can use winetricks to manually create an empty prefix, and try running the installer from a shell or explorer.
Honestly though, a lot depends how the game ran, or how the install worked.
For example, some installers just prompted for a disk change because they wanted “lrgfile2.pak”, which just happened to be on the second disk. Typically it extracted what it needed, then used either disk for copy protection. (see WINEHQ Wiki - Copy Protection)
However, in some cases where copy protection wasn’t a problem, and the files are clearly sequential, you can merge the expected content into a new .ISO or write it to DvD/USB, and the game would just continue.
You can present a mounted ISO or USB drive to WINE, so it’ll just see it as a drive.