Multisite Network menu links not updating

Pat J’s answer is correct but left out one important step.

In wp-config.php the DOMAIN_CURRENT_SITE constant must be updated or the behavior that brandozz explains will occur.

When updating domains for a WordPress Multisite:

1. Update the DOMAIN_CURRENT_SITE constant in wp-config.php

   define(‘DOMAIN_CURRENT_SITE’, ‘my-domain-name.com’);

2. In DB table named “wp_sitemeta” update “siteurl” meta key

3. In DB tables named “wp_{blog_id}_options” update “siteurl” and “home” meta keys
4. Search for remaining links to update in post content with phpMyAdmin or MySQL command line. Be careful when changing links in JSON or serialized arrays.