Ask HN: Browser for individual websites?

Is there a browser that allows you to log in to Facebook in one window (or tab), to Google+ in another, to Twitter in another, etc, such that those windows or tabs have individual/isolated sets of cookies, so that you can browse the web in another window or tab and not have these websites track you?

If such a browser does not exist, would it be relatively easy to modify Firefox or Chrome source code to make it behave this way?