>>19806059There are a few different Pokémon tabletop homebrew systems.
Pokémon Tabletop Adventures, or PTA, was the first. It works but has its flaws.
http://1d4chan.org/wiki/Pok%C3%A9mon_Tabletop_AdventuresPTA's spiritual successor is PTU, or Pokémon Tabletop United. PTU was a spinoff made by many of the people who worked on PTA and it fixes many different problems PTA originally had, rebalancing trainer classes, adding a skill system, and unifying the stat system between humans and pokémon to make combat between them easier to run.
http://1d4chan.org/wiki/Pok%C3%A9mon_Tabletop_UnitedPTU is a fun system, but it's very involved and the balance is not perfect. Running it with more than 3 people is nigh impossible (combat runs on a grid, so a grid with three players is at least each trainer, his/her pokémon, plus enemies), and you need to keep track of a lot of different stuff.
When it works though, it works well. Trainers are competent and play just as much a role as the pokémon themselves, with the class system making them competent in a wide variety of skills ranging from combat against humans and pokémon to pulling off movie-tier stunts.
Both systems are primarily inspired by the pokémon special manga, but there is no definite setting and it can be adapted to whatever the players/gm want.
If you want help hammering out a system, pop in to
>>>/tg/ and ask for advice, we have experience in doing homebrew systems and may be able to offer useful ideas.