I've got a zend site where DocRoot is placed to public/ and URL as (http://dothat.com/controllerA/action9/) - that is working correctly.

I should also operate a copy of this site on a single server as (http://dothat.com/now/controllerA/action9/) running on same folder.

(The web addresses given are good examples)

Please suggest how is this done without ruining zend setup itself.

I'd personally just perform a simple Zend route inside your Bootstrap.

Example:

protected function _initRoutes()
{   
    $this->bootstrap('frontController');

    $frontController = Zend_Controller_Front::getInstance();

    $nowRoute = new Zend_Controller_Router_Route("now/:controller/:action");

    $frontController->getRouter()->addRoute("now", $nowRoute);
}

Routes in Zend are extremely effective and fun to create. I really have mine within an outdoors .ini file to really make it simpler to create, even atmosphere aware.

What about that idea:

An alias in Apache (whether it's the http server you are using)

Alias /now /path/to/zend/public   
<Directory /path/to/zend/public>      
  SetEnv APPLICATION_ENV development
  ...
</Directory>

And you've got to look after the .htacces too

...
RewriteRule ^.*$ /now/index.php [NC,L] 

E.g. with another environment variable for that path within the rewrite rule..