<sup>Answer remade and now working as per the Question specifications.</sup>

To add a menu item to each site of the network if an specific plugin is active in that site, I'm using a [Must Use](http://codex.wordpress.org/Must_Use_Plugins) plugin. It only runs if `is_multisite()` and if `is_admin_bar_showing()`.

In this example, the plugin is instantiated with the following values that check for the plugin Analytics360º and remove all default menu items:

 - *Menu item title*: `Analytics360`
 - *Plugin to check for*: `analytics360/analytics360.php`
 - *Menu item URL*: `index.php?page=analytics360.php`
 - *Remove defaults*: `array( 'newpost', 'comments', 'visit', 'dashboard' )`
 
![plugin in action][1]

![plugin in action][2]

    <?php
    /**
     * Plugin Name: Modify My Sites admin menu
     * Plugin URI: http://wordpress.stackexchange.com/q/55724/12615
     * Description: Add an admin menu link to specific plugin, if it is active in the site. Can remove default items as well.
     * Author: Rodolfo Buaiz
     * Author URI: http://wordpress.stackexchange.com/users/12615/brasofilo
     * License: GPLv3
     *  
     * Class based in http://wordpress.stackexchange.com/a/77236/12615
     **/
    
     
    WPSE_55724_My_Sites_Extra_Items::init( 
    	'Analytics360', // Menu item title
    	'analytics360/analytics360.php', // Plugin to check for
    	'index.php?page=analytics360.php', // Menu item URL
    	array( 'newpost', 'comments', 'visit', 'dashboard' ) // Remove defaults
    );
    
    class WPSE_55724_My_Sites_Extra_Items
    {
        private static $ins = null;
    
    	private static $title = null;
    	private static $plugin_file = null;
    	private static $plugin_page = null;
    	private static $remove_defaults = null;
    
        public static function instance()
        {
            is_null( self::$ins ) && self::$ins = new self;
            return self::$ins;
        }
    
        public static function init( $title, $plugin_file, $plugin_page, $remove_defaults )
        {
    		self::$title = $title;
    		self::$plugin_file = $plugin_file;
    		self::$plugin_page = $plugin_page;
    		self::$remove_defaults = $remove_defaults;
    		
    		if( is_multisite() )
           		add_action( 'plugins_loaded', array( self::instance(), '_setup' ) );
        }
    
        public function _setup()
        {
    		if( is_admin_bar_showing() )
            	add_action( 'admin_bar_menu', array( $this, 'add_items' ), 9999 );			
        }
    
    	/**
    	 * The global var is passed by reference in a do_action_ref_array
    	 */
        public function add_items( $wp_admin_bar ) 
        {
    		foreach ( (array) $wp_admin_bar->user->blogs as $blog ) 
    		{
    			switch_to_blog( $blog->userblog_id );
    			
    			// Current menu ID
    			$menu_id  = 'blog-' . $blog->userblog_id;
    			
    			// Add URL to current-site/wp-admin/plugins.php
    			$wp_admin_bar->add_menu( array(
    				'parent' => $menu_id,
    				'id'     => $menu_id . '-p',
    				'title'  => __( 'Plugins' ),
    				'href'   => admin_url( 'plugins.php' ),
    			) );
    			
    			// Remove default menu items
    			$this->remove_items( 
    				&$wp_admin_bar, 
    				self::$remove_defaults,
    				$menu_id
    			);
    					
    			// Add custom menu for chosen Plugin it active in current site or network activated	
    			if( current_user_can( 'manage_options' ) && ( $this->is_plugin_active( self::$plugin_file ) || $this->is_plugin_active_for_network( self::$plugin_file ) ) )
    			{
    				$wp_admin_bar->add_menu( array(
    					'parent' => $menu_id,
    					'id'     => $menu_id . '-my-p',
    					'title'  => self::$title,
    					'href'   => admin_url( self::$plugin_page ),
    				) );
    			}
    				
    			restore_current_blog();
    		}
        }   
    
    	/**
    	 * 
    	 */
    	private function remove_items( $wp_admin_bar, $items, $menu_id )
    	{
    		if( in_array( 'newpost', $items ) )
    			$wp_admin_bar->remove_menu( $menu_id . '-n' ); // New Post
    
    		if( in_array( 'comments', $items ) )
    			$wp_admin_bar->remove_menu( $menu_id . '-c' ); // Comments
    			
    		if( in_array( 'visit', $items ) )
    			$wp_admin_bar->remove_menu( $menu_id . '-v' ); // Visit Site
    			
    		if( in_array( 'dashboard', $items ) )
    			$wp_admin_bar->remove_menu( $menu_id . '-d' ); // Dashboard
    	}
    
    
    	/**
    	 * WP function uses is_plugin_active_for_network 
    	 * which doesn't work in frontend
    	 */
    	private function is_plugin_active( $plugin )
    	{
    		return in_array( $plugin, (array) get_option( 'active_plugins', array() ) );
    	}

    	private function is_plugin_active_for_network( $plugin )
    	{
    		$plugins = get_site_option( 'active_sitewide_plugins');
    		if ( isset($plugins[$plugin]) )
    		    return true;
    		return false;
    	}
    }


  [1]: https://i.sstatic.net/o0tDH.png
  [2]: https://i.sstatic.net/CwnMR.png