SSO when users share a browser

[snekse]

I'm not sure if this is a Shibboleth question or just a SAML question.

Currently our www site allows users to share a browser because a session
key is contained in the URL and all the links they click on within the site
maintain that key.

Is it possible for users to share a browser and maintain separate SSO
sessions?

My gut says no, but I figured I should check.
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