If you're playing HGSS with a soft-modded 3DS or with a flash card, you can use the homebrew app Pokémon Chest to store and modify your Pokémon. All you need to get started is a monster you want to modify. You can even modify your starter! This opens up new possibilities for playing through the game. This page lists some fun type triangle ideas that will work similarly to the existing Fire, Water, Grass archetype.

Some triangles may be removed as I come up with actual starter combinations.

This applies to 6th gen and beyond.