A recent article on WPMU DEV explained this kind of migration.
As far as I understood from the conversation with Patel, you just miss the second part of Step 4 (single sites db tables).
First and foremost, back up your Multisite installation.
If you haven’t done so already, purchase that fancy new domain name
for your network and associate it with the same web hosting account
that your Multisite currently lives on.
You’re going to need to edit the wp-config file in the root directory
of your site. You can access this either through your File Manager or
FTP. Once you’ve located the file, click on the Edit button to open
it. Now, when you configured WordPress for Multisite, you added some
code above this line:
/* That's all, stop editing! Happy blogging. */
The line you need want to update in this case is this one:
Update “yournetworkname.com” with the new domain name you want to use.
You then need to add the following two lines of code above the “That’s
all, stop editing!” message:
Save your changes and exit.
The database files for your Multisite now also need to change to
reflect the new domain name of the network. Log into phpMyAdmin. From
here, you’re going to need to search for your network’s database
tables. Specifically, these are the ones that will require an update
from the old domain name to the new one (these are all preceded by
blogs > domain
options > home
options > siteurl
sitemeta > siteurl
In addition, you also need to update the following tables for each of
the sites that exist on the network. The pound sign (#) below is where
you will see the actual site ID number.
#_options > siteurl
#_options > home
#_options > fileupload_url
Once you have renamed the domain in every instance in which it appears
throughout your database tables, you can save your changes and close.
Your site should now be fully migrated to the new domain name.
Don’t forget to change the name of your site as well as the web
address within WordPress.