Can I open templates/routes other than 503 when Craft is offline?
I don't think it's possible using the System Status switch in Settings → General.

I had a similar requirement and solved it with a custom variable "maintenanceMode" in my config.php and added some simple logic to the init method in my business logic plugin, which redirects all request except some maintenance mode URLs to the 503 page.

$maintenanceUrls = array('/503', '/impressum', '/about');

if (craft()-&gt;request-&gt;isSiteRequest() &amp;&amp; craft()-&gt;config-&gt;get('maintenanceMode')) {
    if (!in_array(craft()-&gt;request-&gt;getUrl(), $maintenanceUrls)) {
        craft()-&gt;request-&gt;redirect('503');
    }
}