I would stay on my best behavior, charm your parents a bit,show them that you are responsible and that your attitude will stay in check under many circumstances then calmly strike up a deal set the peircing as a goal to acheive somthing they want (ex.Good Grades). So in the end everyone wins. In the end the answer would differ from the parents.
Also you could show them pictures of celebrities with multiple ear piercings. Some (Hilary Duff, Rihanna, NOT Kate Moss or Fergie) look very classy. Don't make it obvious you are showing the earrings, incase they get more annoyed. Try to show them that multiple ear piercings can look very pretty.