You have at least three options:
- use a Child Theme on mysite.com, in which you replace index.php with whatever you want
- Use a different Theme entirely on mysite.com – could be a landing-page Theme or whatever.
- Use your current Theme on mysite.com, but set it to display a static page as front page, put your subsite links in the page content of the page displayed as the site front page, and remove all other content