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In Heroes of Might and Magic III, there were 4 schools of magic, but in Heroes of Might and Magic IV, they expanded it to 5 (penta-) schools of magic. Moreover, each school is unique and doesn't overlap much, essentially utilizing all the elements. Both in Heroes of Might and Magic III and Heroes of Might and Magic IV, the system of magic schools is well-structured. I don't see any element that could be used to create a new school that would harmoniously fit into the existing pentagram.