Output cells for 'Anyone with the link can "execute" this project'

Sharing a notebook with execute permissions is almost a fantastic workflow for my class notes, with one exception: I believe that currently all users executing the code write into the same shared output cells.

Suggestion: can each user generate their own output cells (not shared across users)?

Reason: in my notebooks, I print into the output cell a unique URL that the users must point their browsers to (using the new tunneling feature!).  If users execute the notebook, then they could get someone else's URL.  I have an example notebook here: https://deepnote.com/project/intro-bjLOEOQGQCar-wC-eMR4yw/%2Fintro.ipynb 

Admittedly, I cannot currently think of a workflow where sharing the output is helpful, and might have missed something in my thinking.
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