Clear spheres let you remove any non-optimal stat-up nodes and replace them with optimal nodes, therefore using up less space, allowing you to have higher stats. For example, if you have four Strength +1 nodes, and use four Clear Spheres on them. When you put a Strength Sphere on one of the now-empty spaces, you have the same stat bonuses, and three extra spaces to increase your stats beyond what you could have achieved while the four Strength +1 nodes were on the board.
As for maxing everything, it can't be done. You would need well over 1000 nodes to reach the maxima of every stat (330 HP, 250 MP, roughly 60 for the others). The sphere grid, even the Standard one, does not get close to that amount, especially when you take out the 86 nodes dedicated to Command Abilities which cannot be cleared.




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