Organize template page-XXX.php files into sub-folder?

Hello everyone,

I’m working on a template that required quite a few page-xxx.php files and l was curious how l could go about putting these files into a sub directory of my theme to make things more organized for anyone who works on the site after l’m done.

For example, say l have:

path/to/theme/page-signup.php
path/to/theme/page-members.php
path/to/theme/page-records.php
path/to/theme/page.php

But wanted it to be:

path/to/theme/page.php
path/to/theme/page-tempaltes/page-signup.php
path/to/theme/page-tempaltes/page-members.php
path/to/theme/page-tempaltes/page-records.php

Any quick & easy ways to accomplish this?
Thanks to anyone who can offer insight.

Regards,