Allow users to create projects, but only based on a shared project?

[Esther Strom]

I've been our Jira admin for 7 years, but we've always been a small company (fewer than 100 employees), and none of the other users wanted to create their own projects, so I've been able to keep pretty tight oversight on things.

We were recently purchased by a larger company, and I already have people asking me if they can create their own projects. I don't want to open up that permission to everyone, and even people who should be allowed to do so should be restricted to a certain degree.

I have a set of "template" projects that have customized workflows, issue types, etc. When I create a new project (for most teams), I choose to have the new project share settings with an existing project, and choose one of the "template" projects as the base. 

Is there any way I can set up permissions to allow a certain user group to create new projects, but only if they select one of the template projects to share settings with?

I'm open to using an add-on if there's one available. We are on Cloud.