well to do it for characters, you would likely either have to manually edit their AI with something that causes them to level up in battle (and give them a specific growth there, reading in the exp values of the enemies they kill and adding it to a global variable or whatever), making any level information they have in the main menu useless/inaccurate, which is likely what you do not want, or completely rewriting the game's level-up code for the party members (likely within the .exe), both of which would likely take a long time to do (you would have to find the data in the .exe first, and it could potentially cause issues elsewhere if the size was made to be larger, as you would likely have to repoint everything), and both having potential downsides.
enemies, however, can be made to go over level 99 naturally, and a level 255 enemy with 255 attack will be dishing out slightly over 30,000 damage (capped at 30,000 with the new damage cap) with a BASE power attack
. and if enemies and characters have the same level cap (255) it would make it harder to keep the game difficult, as the only real difference between your party and the enemy would be HP and abilities, while your party capping off at 99 means that enemies can be simply boosted a few levels, even with the same stats, to cause more damage (though to make them live longer, more def/mdef/HP would be needed, but that is besides the point
).