@Elder01 PKHeX allows changing of Ability, if that species has more than one ability number,
Example:
However, if you're referring to changing the ability to an illegal ability, it can't be done.
Not because the feature isn't implemented, but rather it is a limitation of the Gen III games.
In the Pokemon data structure, the ability is determine by a bitflag: 0 for ability 1, and 1 for ability 2.
The game then checks against the game data, to assign the correct ability to it.
Look at the data structure here:https://bulbapedia.bulbagarden.net/wiki/Pokémon_data_substructures_in_Ge