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I like watching a couple of games at once as well so I don't miss any of the action! The New NHL.TV Player which uses HTML5 doesn't have the feature yet. To toggle between Single, Picture in Picture, Dual, or Quad view. You will need to switch back to the Flash Player version.
To do so, select Settings found at the top right and then, Go back to Flash Player. Once there, you should see the View button you're looking for.