Migrating single blogs (cPanel subdirectories) to Multisite in subdirectories

Is it possible? The how-to in the Codex explains how to do this using subdomains but I’d much prefer directories.

The existing sites are all domain.com/bloginstall on cPanel hosting (public_html/bloginstall).

I’m setting up on a new host and plan on building a Multisite network of them before changing the DNS to point to the new space.

I’d really like them to start as domain.com/bloginstall rather than change to bloginstall.domain.com but can’t find detailed instructions anywhere that suggest it’s definitely possible.

I have some experience of migrating WP sites and have functional skills in phpMyAdmin and editing individual core files.