A little self-promotion: for sites that limit the number of articles you can read, I recommend the Firefox add-on ("Open Page in Private Window") I developed that will open the current page in a new private/incognito tab.

The use case: you load a news article, hit a "you've used up all your free articles this month" overlay, so you click the "Open Page in Private Window" toolbar button to view the article in a private tab.

https://addons.mozilla.org/en-US/firefox/addon/open-page-in-...