How to Change PHP Code for Child Theme When File is Below Parent Theme Folder?

I have had success in copying a php file from the parent theme (wp-content/themes/<parent_theme_name>) to the child theme (wp-content/themes/<child_theme_name>) and then modifying the file when the file resides at the top folder level.

But now I am trying to customize php files that are below the main theme directory (such as wp-content/themes/<parent_theme_name>/inc) and I am not having success. I create a similar directory structure under the child theme, copy the file, make modifications to the file, but the changes don’t take effect. I know that the changes work, because if I make them in the parent theme, then they do take effect. It is only when I make the changes under the child theme that they seem to be ignored.

Does anyone know if it is possible to modify a php file that is below the main theme directory (wp-content/themes/<parent_theme_name>?

And if so, how?