Second wordpress installation on subdirectory

It’s probably not the best idea, but you can absolutely create a second install in a subdirectory.

If you create a /blog subdirectory and install WordPress there, you’ll have a whole new site, with a whole new WP dashboard.

example.com/wp-admin/

and

example.com/blog/wp-admin/

You could set up the new WP config to read the WordPress core from the parent install, allowing you to only install the themes/plugins you need for the secondary install.

Honestly, Multisite is probably a better idea — you’ll be able to manage both sites from the same dashboard — but what you’re trying to do is possible with either approach.