SSL on sub subdomain multisite setup

I have a WordPress multisite setup as subdomains of a subdomain, i. e., The main site is at site.domain.tld and my sysadmin has installed a wildcard SSL for *.site.domain.tld. All of the sites in the network are secure but the main site at site.domain.tld is not and gives a warning with this setup. This is problematic as users login on the main site to access their other sites and having a big old security warning is not cool. How can one go about securing the main site and the network sites? I have the same setup on my personal DreamHost VPS that I use for testing with the addition of Domain Mapping in the mix. I'm just now trying to play around with securing the DreamHost setup as a way to test the work related setup.

Not sure I can grant access to the site as my sysadmin has the login set to require people to have a campus IP.