Like the title says. Is this possible? If not, why not? If yes, how do I do it?
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Both people will have to register for an account (using different openIDs). Each user will have to log out when they are finished with their session.
When I've dealt with this before, I usually created a separate computer account (windows user) and that way they had to log out of their windows account, but they had their own bookmarks and cookies, and didn't have to log in to their various websites again.
Another alternative is to install Safari, Chrome, or Firefox and have one person use one browser, and the other use a different browser.
Another solution if using Firefox is to create two profiles inside Firefox, and switch between them with ProfileSwitcher extension.
Edit: from @xport question's comment Multifox does the same and seems easier.