This is random but a really neat idea just crossed my mind.
What if in a future gen, Pokémon could have multiple possible shinies? Each Pokémon would have their normal coloration, but also eight possible shiny colorations. So if you get, say, a Shiny Ralts, it could be a number of possible colors, not just blue.
The base shiny rate would be increased to 1/512. This way, the 1/8 color roll stacks on top of it so that the individual shiny colors still have the usual 1/4096 odds. This way, if there happens to be a particular shiny color that you really like, hunting for it is the same difficulty as hunting shinies is already.