There are many elements of a Shakespearean play that could be changed in order to make it more accessible to a modern audience without changing the meaning of the play. This depends on the particular characters and play we are talking about. Some of the institutions could be updated. For example, instead of a king, the play could show a president, without altering the significance of power struggles. Moreover, the language could be adapted in order to better reflect the way English is spoken in modern times.
A lot. The words could be modernized without effectively changing the meaning, the setting could be changed to any time period and the message of the show would come across. Certain characters could be gender-bent, etc.
