Had an idea for a playthrough challenge, almost a modified Nuzlocke. It would be easier in most ways, but similar in the “random encounters determine your team” aspect.

So, the rules would be:

1. You must attempt to catch each species of Pokémon you encounter, which you have not caught before.
2. When you catch a new Pokémon, it becomes a permanent part of your team.
3. You must make a genuine effort to catch a Pokémon species you do not have.
4. You may not have multiple of a single species, but you are allowed to catch multiples.
5. Once a Pokémon has been caught and added to your team, it cannot be replaced, except by a shiny Pokémon of the same species.
6. If you fail to catch a new Pokémon, you are not required to seek it out again - you must only add that species to your team if you encounter it again while there are open slots on your team.
7. You may grind a location and attempt to avoid encountering wild Pokémon in order to influence your team, but again, if you encounter a Pokémon you’ve never caught, you must attempt to catch it, no matter what.
8. For this purpose, members of the same evolutionary chain count as the same species - if you catch a Bidoof, and later encounter a Bibarel, you cannot catch the Bibarel, even if your Bidoof has yet to evolve.