The only way to increase further is through attribute cards, they increase your
base stats (the grey part). The green part is what's increased due to
moves. But be careful, any attribute card spent is gone forever, and your base stats cannot go past the cap or below 30. I use this to my advantage for my Judo CAF, his kicks are already at 30 so a Freestyle Wrestling card with -4 leg power will not decrease his leg power at all haha