Very interesting question. I’m not sure whether this can be done exactly in the way you want, but there are some alternatives and possible approaches.
The very easiest solution is not exactly what you asked for: put the new primary website at another subdomain or domain/TLD (i.e. .info instead of .com), and add a redirection from only the homepage of the old multisite to the new primary website. But it’s not optimal for SEO having a redirection at the first homepage level, and may also mess up the branding in some other ways.
The next easiest solution would be moving/renaming the multisite to a subdomain (it’s not that easy, but still easier than your wanted solution), and adding some redirects for /subsite1 + 2 + 3 on the primary website. Still not exactly what you asked for.
Another solution is transforming all subsites into individual WP installations, in server subdirectories of the primary website, matching the paths /subsite1 + 2 + 3. There some tools out there for such a task, like Duplicator Pro. Problematic if you need the users to be kept logged in on more than one subsite, maybe with the plugin “WP Remote Users Sync”. And its more work to update them all, maybe use “MainWP” or another central administration tool for multiple installations.
Your wanted solution requires the multisite to be moved to a server subdirectory of the new primary website under domainname-primary-site/multisite-main (or whatever you like as path for the multisites main site, which now has no other content or function beneath beeing the multisites main site), and adjusting the subsites urls paths and cookie paths in the database and config file, and maybe also some adjustments in the .htaccess of the primary website.
This may be an approach: https://wordpress.stackexchange.com/questions/119493/multisite-in-subfolder-how-to-make-new-sites-to-be-in-same-level-subfolders-as
Tricky – if you want to do it manually, I recommend to exercise it on a copy of the multisite or at least an independent test installation.
Or if you use NGINX, you may use path-based routing to keep the new primary website and the old multisite devided. But you still have to move the multisite’s main site out of the path from the primary website…