What about a game where you can summon Pokémon using your mind or spirit? Something like the Stands from Jojo's Bizarre Adventure,

There would be a character for every Pokémon but you,who can use every single Pokémon in the game including legendaries. These Pokémon can be obtained killing the person who use that Pokémon and absorbing his/her soul.

The way you summon your Pokémon is using a device in your head that stimulates your brain to free the Pokémon from its spiritual jail.