A common question I am asked is about “Shared with me” in Google Drive. This is a filter, not a folder. You can not organize files in “Shared with me,” nor should you consider this a place to keep shared files.
Move Files
I frequently click on “Shared with me” (also with “Recent”) to see what is there. I then single click on a file and press the Z key to MOVE it into a folder so it is organized where I need it.
Add Files
I would recommend getting into the habit of using SHIFT Z instead of z.
Shift Z ADDS files to a folder. This means it can live in multiple folders. Using shift z prevents you from accidentally moving it OUT of your collaborators folder.