I suggest that characters be able to "power down". What I mean by this, is that whenever a character fights, they should choose what percentage of their power they would like to use. 100% is basically your base stats on your player card, but anything lower than that is, well, lower.
For example, if I were to use 30% of my power, my damage and speed would go down to 30% of my base damage and speed on my player card, which would make it easier for the more powerful characters to train with the weaker ones in a canon-DBZ way. The powering down would only reduce damage and speed, have no other effects, and would be completely normal after the battle ends.