I would stay true to the Shakespeare language but I would also change the setting into a more modern setting and add more colour to the scene, for example have the characters wear more colourful and extravagant clothing.
In certain scenes I will use the technique that Baz Luhrmann calls vortex. This is where you place the characters in themiddle with a crowd or objects surrounding them.
To direct certain scenes I will make use of filters. the filters willput emphasis on certain scenes like the scene when Antony receives news from Rome and tries to dismiss it but Cleopatra insists that he hears the news.