So you can change nature gains, stats and abilities with mints, bottlecaps and ability capsules/patches, respectively. What do you think GameFreak will never allow you to change?

>Shinyness: Would make shinies worth less and would make no sense from a lore perspective
>Actual nature and characteristic: Would be changing a Pokemon's personality, and would make mints pointless.
>Gender: Would encourage mental illness and would screw with the PID
>OT and TID: Would ruin the sentimental value and to prevent event mons from being changed
>IVs: Would make Bottle Caps pointless

I could see them eventually allowing you to change the caught Pokeball (under certain conditions) though and possibly making an anti-Bottlecap that decreases stats.