Building several projects with Gitlab CI at once

Hey there,
we are heavily experimenting with Gitlab CI and automated builds. It’s
working very well: The .yml file is picked up from the runner, shell
code is executed and it’s awesome that you can remotely trigger builds
from something like this:

<html>
  <form action="https://.../api/../projects/../trigger/builds" method="POST" >
    <input type="text" size="20" value="e5...3c" name="token" />
    <input type="text" size="20" value="master" name="ref" />
    <input type="submit" />
  </form>
</html>

At my university of applied science, we organize an internship for our
students. During that internship the students have to code a proper
http-server as an exercise.

We came up with the idea to implement a tool/feature in Gitlab to build
and test all these commited student-servers at once on one day of the
week.

I think GitlabCi with its Runners/Triggers/.yml etc provides a great groundwork for our plan.

Now, how would you do it? Where could we start?

Does the Gitlab API provide enough scope for this?

Thanks a ton in advance.