"Hungry Bill"
1. If a Pokemon faints, it's dead, and must be boxed.
2. You may not get Pokemon OUT from the PC. You may box them (effectively killing them). Thus, if you white out, Game Over.
3. You may only catch the first encounter in each area (making exception for Rule 5, if playing by it).
4. After each Gym badge you earn, you must box your oldest team member.
5. Name each Pokemon by the order you got them (Starter as 0/Zero, first capture as 1/One, etc.) to keep track.

Optional:
6. Box all gift Pokemon (Eevee, Lapras, Castform, etc).
7. No items may be held or used (obviously excluding balls).
8. Box a team member after Rival battles.

The idea behind this is obviously to make the run more challenging, but also to make the player train more than one Pokemon.
It should also make him/her think ahead, in the same way as a 6mon run would, but with a maintained element of party instability throughout the whole run.