Single volumne 7-Zip archive could be extract by this code:
Nsis7z::ExtractWithDetails "ArchiveName.7z" "Installing package %s..."
How do I extract multivolume 7-Zip archive using Nsis7z plug-in in NSIS Installer? File name is file.7z.001, file.7z.002, file.7z.003.
Not a programmer, but if you find yourself wanting results and I'm the only one who's replied for any amount of time, you might try this, see what comes of it.
I don't know where to put it in the code, that code looks foreign to me, but wherever you define the input archive, instead of name.7z, put, as you say, name.7z.001. Now, a lot of archiving programs will detect a split archive and automatically move onto the next one. They should be joined like that. So your plugin should work the same way.
But again, I'm not a programmer, it just seems like that's how it'd be, based on my experience working with archives. Sorry if it doesn't help.