Can't think of a fully automated way to do it now. That would be possible when simple coding logic will become available to users, so one will be able to execute loops to iterate over each selected clip.
I can suggest a workaround to move one clip to specific track to playhead option (with idea that it is placed on first track):
- Keyboard Shortcut: Nudge Clip selection up (multiple times to get proper track)
- Move Clip to Playhead
This way, you can create 3-4 user commands to move selected clip to track 2, 3, 4, to stack it up. Though you will need to select each clip manually.