Here's a simple guide for you to change a base domain name or site url for WordPress and MPMU.
1> Go to the below link to download a tool which named Search-Replace-DB to your local.
2> Upload the tool script folder to your site root folder.( eg. the same folder as wp-config.php or wp-content.php)
3> Browse to the script folder URL in your web browser.
4>Fill the fields as needed.
5> Click the "live run" button to start searching and replacing.
6> After you replaced, please delete the script folder in your account to secure your account.
7> Edit wp-config.php, replace old domain with new domain if it has site url settings.