Yes, you can create as many subdirectories within subdirectories as you like. Learn how to create a subdirectory.

Tip: Before you create a subdirectory, be sure to navigate to the folder in which you want to create it. For example, if you want to create a new subdirectory in a folder called sample_folder, click the "sample_folder" link in File Manager to open that subdirectory, then create your new subdirectory. You can check the topmost blue bar of the File Manager to make sure you're in the right place. You'll see something like this:

yourdomain.com > sample_folder