That's very cool, Malcolm! There were many things I had already thought of, some things I liked and would like to apply to my system, and some things that I think might tilt balance.
The multiclassing idea is quite genious. I had tried to come up with a parallel, then I gave up and decided not to include it. But Pokemon that have been bred is a great idea! In the Pokemon traits block, it will include the Pokemon's egg groups, and then if you want to pick a "multiclass" feat, it must be of a Pokemon from the same egg group, and you can only pick feats of one Pokemon. Thank you for that idea!
I also thought of this. Trainers (being only the equivalent of a race) don't get feats themselves, but their Pokemon can choose feats that give a bonus to their trainer rather than the Pokemon. For example, one feat might increase the distance the trainer can throw Pokeballs, or could affect the trainer's skills. If you think of it as a parallel to D&D, it fits! When you trade Pokemon, if any trainer feats don't meet the prerequisites of the new trainer, they can be retrained immediately.
The way you did paragon paths and epic destinies is where I think balance will be skewed. Each Pokemon has no more than three evolutions, and there are three tiers, so the first tier is the Pokemon's lowest evolution, the second tier is the Pokemon's second evolution, and the third tier is the Pokemon's highest evolution. The way I see it, each Pokemon should get their own epic destiny instead of two paragon paths, because they don't have the same effects. However, those paths or destinies might apply more to the trainer than the Pokemon, just as the Pokemon can pick feats that apply more to the trainer than the Pokemon (see last paragraph).
I'll post what I have for Bulbasaur in a second, because I think it's interesting how we have different ideas of how it fits into D&D roles.