Not sure if this is a bug or a feature but i cant level my pokemon above the lvl my current pokemon badge is. It is however regularly commented upon ingame and i have read from several other players on here that at least in former versions it was possible to do so so i suppose it should be possible to go beyond the level cap even if you havent got the badge yet and just have your pokemon not listen to you. I find this extremely frustrating as well because i always reach the cap way before im done with the arena/area etc. so i just run around not gaining any XP. Also the fights are incredibly hard since i cant level any pokemons above the enemies. I really enjoy the game so far, but this just makes it unnecessarily frustrating. Reborn wasnt half as hard.