No you cant do that as you can have multiple instances running on the server.
But you can of course do re-directs using unique FQDNs. That is what we do. We create a FQDN for each site (and you only have one) and we use Apache re-directs for that. We also do http->https for obvious reasons.
cat /etc/httpd/conf.d/redirects.conf
RewriteEngine On
RewriteCond %{HTTP:X-Proto} !^https$
RewriteCond %{REQUEST_URI} !/server-status
RewriteCond %{HTTP_HOST} !^localhost$
RewriteRule (^/$) https://%{HTTP_HOST}/ [L]
Header set matched true
<Directory /var/www/html>
# mysite.mydomain.local
RewriteCond %{HTTP_HOST} =mysite.mydomain.local [NC]
RewriteRule ^(.*)$ /checkmk_site/$1 [L]
</Directory>