Multisite with different domain names

WordPress Multisite can handle this without a plugin.

What you need to do:

I’m assuming that your WP Multisite installation is at example.wordpress.com and your desired URL for the new site is example.com, per your question.

  1. Create the site in the Network Admin section on example.wordpress.com.
  2. Select Edit Site on the newly-created site.
  3. Change the Site Address (URL) to whatever you need it to be (in this case, example.com.

As long as the DNS resolves correctly, and your webserver knows that example.com is to be served by example.wordpress.com (eg, your example_wordpress_com.conf file in Apache has a line like ServerAlias example.com), you should now be able to go to example.com in your browser and have your new site appear.

See this answer for a couple of screenshots.