WARNING: It’s dangerous to mess with a CMS’s mod_rewrite as it’s tied into the module which reads and parses the URI to fetch the correct modules and data for the visitor.
Okay, it IS possible but dangerous. IMHO, what you need to do is the “loopy” redirection which is discussed as an example near the end of my signature’s tutorial. Use the {IS_SUBREQ} version and be sure that you’re redirecting away from component/estateagent with an R=301 then redirecting back WITHOUT the R=301 (so Joomla can serve the correct file).
# Assumes "usable link" is index.php?id=alpha
# and alpha is the extensionless link
# Redirect to NEW format
RewriteCond %{IS_SUBREQ} false
RewriteCond %{QUERY_STRING} id=([a-zA-Z]+)
RewriteRule ^index\\.php$ %1? [R=301,L]
# Redirect back to "usable link"
RewriteRule ^([a-zA-Z]+)$ index.php? id=$1 [L]
I’ll let you add the case directory to this with the reminder that “case/” is the NEW format while “component/estateagent/” is the serve-able format.