In general, it is possible to integrate several other WordPress websites within one WordPress directory. Whether this is always the best way is open to question.
If you name the subdirectory for the additional WordPress installation e.g. /intern/, then this name must not be used for a subpage in the parent WordPress installation, so that there are no conflicts.
In addition, the .htaccess file in the subdirectory must be adjusted as explained below:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /intern/
RewriteRule ^index.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /intern/index.php [L]
</IfModule>
# END WordPress