There is no menu command for the Photoshop layer comps but there is a panel in the window menu. Display the comp panel.
A document can have a single or multiple layers and you can store the position etc for those via the panel. Go to the right side menu and select the new command (or click the + at the bottom of the panel). You will see the following options : visibility (default) as well as position and appearance ( styles) and smart objects. You can also add a comment. To store the information, click the entry such as position so any movements are recorded. As soon as you click OK you will see an entry in the panel. You will see the entry listing the current stored details.
You can select any of the entries and then click the left side box and the entries will be restored back to the recorded state and uses the properties stored so if you have a style, it will be replaced with the old one.
You can use the arrows at the bottom to move between the entries. You can also move between the entries by just clicking the entries in the panel or use the right side menu to apply previous or next
You can keep the entry selected in the panel and then move objects, change styles, opacity etc and then click the third / fourth / fifth etc entry at the bottom to update the various properties. You can do the same with the right side menu update commands. The seventh button updates everything for the current entry selected.
You can use the delete the entry at the bottom of the panel (on right side menu delete command)
Create a document and add some entries to it via the panel (such as the appearance, position etc) and save it as a PSD etc file (as long as it stores the data). Go to a new document and file menu and place linked and select that file and it will be displayed as a smart object. Create some new entries in the panel and record this data by re-positioning, appearance etc but you can also go to the properties panel and select the entry you want to use from the placed document (so you will the entries from this document and the entries from the other document to work with). Not sure if this extends to linking to three or four levels of document.