Theme Folder with Subfolders

I am managing a website that has a bunch of theme templates.

so under wp-content/themes/mytheme/

there are dozens of template files. This makes it hard to organize. I was wondering if I could create a subdirectory structure

wp-content/themes/mytheme/teacher/
(contains 10 or so templates)

wp-content/themes/mytheme/admin/
(contains 5 or so templates)

wp-content/themes/mytheme/plans/
(contains 12 templates)

I want the subdirectory structure to work with

Template Name: name

Is there a way to do this. I tried just creating the directories and putting the files in and it did not work

Any ideas?