Increasing limits can be tricky, even to the point where despite being able to explain why it is tricky and work around the issues I would sooner come the other way for most things and decrease damage, move costs and whatever else instead to effectively make the same thing in game, even if it is going to be a lot of work.
Anyway two main issues
1) You might have to get the game to display more than 999. This can be easier said than done, though you might also be able to overflow things (some games will crash if it encounters, some will display some corrupt graphics, others will just display the previous maximum but treat it fine.
2) The data section set aside for it, as well as any functions doing maths on it, may not store that much higher. If you have ever wondered why a lot of stats in games top out at 256, 512, 1024 or something else in the power of 2 sequence then it is because games don't store things in decimal in the vast majority of cases and instead use hex. 999 to 1024 is not a big jump so a lot of game devs just used enough bits to store 1024 and then capped values at "999 or current max health/ap" for other purposes in the game (if inns, potions and whatever else that restores health don't go past it then it should not go past it, you also get to figure out whether each individual restoration tops out there or if it is a more general approach). Some of those might use a strange number of bits compared to the full 16 bits you might imagine, though the other bits can also be used to indicate things (only need one bit per state)
Still you might try finding the max health value; can be found similar way to making conventional infinite item/health/mana cheats, just a bit more tedious and most will probably want to find the experience value and then use it to power level, though might just be somewhere with the rest of the stats. Hopefully it is not a calculated thing (think "take constitution and multiply by level number"). Anyway if there is a max value that the current HP plays to (that can also be a thing to find it if you want to do some proper tracing -- using a potion or something to heal* and somewhere in the mix it will probably check against max health to figure out what to do) and you find it you can try setting it to something silly, repeat also for AP or whatever else you want to break the max limit of. If something silly works then you can hardpatch the cheat, or you can go in deep and make a further analysis to make a nice hack.
*make sure you are not at full health for this as full health might do something different to normal.