Taking suggestions for grading rubric for multiple answers test
One simple way to design a grading rubric for this situation is to consider the question as though it were a set of true-false questions.  So if there are 5 answer and the question is worth five points, then there is 1 point for marking each true, and 1 for not marking each false answer.

Thus, for example, consider the following question: 


  Which of these are mammals? (5 points)
  
  
  Cat
  Turtle
  Lizard
  Fish
  Dog
  


If the student marked "Cat, Turtle", then they would receive 3 points: they lose 1 point for marking "Turtle" and 1 point for failing to mark "Dog."