You basically need to get each link as its own document then do a get these revit links from that linked document. I think this post will help you get towards your goal.
If you are after going even deeper then this i would suggest creating it in python and utilizing the “background Document Open” method, while creating a loop until all links of links has been got(maybe better as a python class/function).
When ever i utilize this background process i usually open a blank project(eg template) so you do not get any issues of opening a file that is within the original document error message.