For argument mapping, add arrows that aren't red or green
Dialogue mapping is used to help groups discuss wicked problems. MindMup is fantastic for this purpose! The only thing that dialogue mapping requires that MindMup doesn't already have is the ability to insert questions and answers. This could be easily accomplished by simply creating an arrow that isn't green for "pro" or red for "con," but is (perhaps) blue or black for "is an answer to the question" or "is a question that is prompted by the above."
I've been using MindMup to map dialogues on my campus already (using green arrows for "is an answer" or "is a question") and people are interested in the method. An additional arrow type would be make dialogue mapping even clearer.