Enrollment restriction on a class-by-class basis

Summary

How to restrict enrollment by group for one class but not others?

Content

I see that Learn has the feature to restrict certain groups from signing up for enrollments (as detailed in the Online Help, page Enrollments > Enrollment Group Permissions) but that this applies to the whole LearnCenter.  Is there any way to designate a subset of enrollments as restricted to one specific group, but allow all users to sign up for the rest of the classes?

Also, is there a feature like this for courses, to restrict them to just one group?

I know that it's possible to put training on pages in the LearnCenter, and restrict those pages to be visible only to certain groups.  However, this won't work for us as we rely on Search and the Catalog widget to direct our users to find training.