Can Shakespeare write a Greek tragic story?

Many of his plays make William Shakespeare household name. How can his tragic novels doesn't fit Greek's characterization . One of the most rational reason is : he is not in ancient time. Many historians conclude that Human being's life standard has changed over time, therefore audience in Shakespeare don't  pay much attention to those elements of Greek Tragic hero. Wait a minute! Somehow William accidentally used one of the factors that most of his audiences favored;it is noble status. Recall that people loved to hear the stories of monarch. Even though his plays doesn't contain all the Greek's characterization of tragic hero , he is influenced by it somehow.