I am trying to connect my local wordpress multisite to my staging database. It works perfect when I am not on a multisite but with the multisite I can't find a way to change the value of the main domain url...

I have tried altering the define( 'DOMAIN_CURRENT_SITE', 'mywebsite.local' ); but it doesn't work.

Any idea on how to go about developing locally a multisite while sharing the database with the staging environment?

Edit

To make it work on a single site install I just alter a bunch of constant to change the main directories url like so:

$domain = 'mywebsite.local';
$directory = 'subdirectory' // only when needed;

define( 'WP_SITEURL',       $domain . $directory );
define( 'WP_HOME',          $domain . $directory );
define( 'WP_CONTENT_DIR',   $_SERVER['DOCUMENT_ROOT'] . $directory . '/wp-content' );
define( 'WP_CONTENT_URL',   $domain . $directory . '/wp-content' );
define( 'WP_PLUGIN_DIR',    $_SERVER['DOCUMENT_ROOT'] . $directory . '/wp-content/plugins' );
define( 'WP_PLUGIN_URL',    $domain . $directory . '/wp-content/plugins' );
define( 'PLUGINDIR',        $_SERVER['DOCUMENT_ROOT'] . $directory . '/plugins' );

Thanks for your help!