Theoretically, you could do this using session_id() and a database entry, although security will be tricky since a malicious user could try generating random session IDs to mimic a logged-on user's session.
Session information is stored in a cookie in the client's browser, with a specified ID. By storing that ID and a JSON string of the data, whenever it's updated, various users could conceivably share the same data. They'd all have to poll the server once in a while to see if the data has been changed.
But at that point, you don't need to use $_SESSION
anymore, so it's pretty much defeated the purpose of your question. You can get the same behavior with regular variables, which would already be a security improvement.
Short answer: No, that's not the point of sessions.
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