How to tweak page links in WordPress Multisite

I fixed it changing the urls of the sites to include the /blog/ suffix. You cannot create the site with a slash but you can change the site URL once it is created.

Then changing the RewriteRules in .htaccess to:

RewriteRule ^([_0-9a-zA-Z-]+/blog/)?wp-admin$ $1wp-admin/ [R=301,L]
RewriteRule ^([_0-9a-zA-Z-]+/blog/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/blog/)?(.*\.php)$ $2 [L]

Finally, adding some code to wp-config.php to properly define the PATH_CURRENT_SITE and BLOG_ID_CURRENT_SITE variables:

define('PATH_CURRENT_SITE', $path_current_site);
define('BLOG_ID_CURRENT_SITE', $blog_id_current_site);