I just got what you meant, forgive me for being slow. To my knowledge they do not have a PvP were you can gain BP anymore. You can' like Gen V fight with some one to defeat the battle masion in a Co-op fashion. Also regarding the BP raise, in the normal battles (single,double,triple,rotation, and Mulity) you gain 1 BP per battle, the after you have your 10th battle it is set to 2 BP per battle, and once you beat the boss (Battle 20) you get 20 BP, so a total of 48. In super battles it starts a 2 BP per battle, after that i don't know but instead of 20 battles until the boss it's 50, And the bosses use non-uber Legendarys.