I always thought that alchemy worked in such a way, that you could discover unlisted combinations of ingredients to make virtually all potions in the game.
That is not true however; brewing something that is not on the list results in fireballs all the time.
For characters with the skill, there is already a guaranteed recipe for PoGA, arguably the most useful potion in the game, though of course achieving 100 skill in alchemy to get it is no easy feat if you're anything else than a wizard or perhaps an assassin.
Additionally, it usually requires other uncommon ingredients to make, notably potions of strength and youth, but not every time.
Other potion recipes are also guaranteed, I don't know the exact list but there are potions of youth/longevity/cure poison/extra healing/insight... only their order of appearance and required ingredients vary.

My suggestion is to add several recipes for other potions.
Maybe make it so that another recipe is uncovered with every 5 additional points in the skill instead of 10.
That still wouldn't be even close to covering them all but it would be a start.
Recipes could also be introduced as a variation of scrolls.
Those could be obtained via quests (like additional Thrundarr's quest for 1-2 alchemy recipes) or rarely randomly found, starting from DL 8-10, so it would be possible to occasionally get one in DT shop or UD.

Of course, not all characters have the skill.
How to handle this issue could potentially bring out very divided opinions, with people on both sides most likely arguing passionately. There could be tears.
Hence, I will make a few suggestions of my own:

1) Add 10 more semi-random recipes to alchemy skill (the list is probably determined at the start of the game) with ingredients equally difficult to find as is the case with existing ones. New mix available every 5 points of the skill, leave everything else as it is.

2) Add recipe item to the game and make it possible to get recipes for ALL potions in existence.
Player could either have them added to alchemy list, or be forced to carry them around or simply memorize them.
If they have never been found, trying to brew the potion even with proper ingredients but without the recipe would still result in a fireball, like the case right now.
Successfully brewing a potion would have a 10% (or variable) chance to teach alchemy skill to the PC in question, if Le and Ma attributes are sufficiently high (15 points each? maybe a sum of both has to exceed 30? wild guessing here).
Skill would start at 1, dice would depend on Le and Ma as well as PC level and successfully creating more potions would train alchemy.

3) Make one of the existing NPCs be able to teach the PC this skill in exchange for a favor/gold/item. Also extend available alchemy recipes as described in point 1)

Personally, I'd lean towards the second option so that is what you would vote for if you press the Yes vote button ;)
In conclusion, 2nd suggestion makes alchemy learn-able but not easily trained, not OP, the list of recipes would be vastly extended and many potions normally discarded would find use.

There could be a mix of all of the above if that is the preferred option.
This feature would also create an additional incentive for melee characters to increase that Le and Ma to required values and obtain the skill.
Occasionally, being able to brew a potion of cure sickness, cure poison or healing would have a chance to save PC's life.
Another benefit and game improvement that this RFE has the potential to introduce, is that all those useless or near-useless potions of boost charisma, stun recovery, berzio, unused herbs etc. would possibly find a reasonable use.
Right now they pretty much land on the floor upon next sorting through inventory or a visit in a store.

I also understand that alchemy fireballs are somewhat popular and cheap method of dispatching certain monsters if all other means fail, but this was not the intended use of the skill and we all know it.
Mixing water with water doesn't create fire. Yes, the manual description says something about 'magical' potions but at the same time we have the assassin that starts with the skill and it's not a particularly magical or even clerical class.
Just a killer that likes to use poison and make it from all kinds of stuff.

One last thing to consider is something JellySlayer spoke of in the thread about Detect Item Status and Ruun: making a skill obtainable via training (or a quest) like point 2 (or 3) suggests, would mean that any character could learn it and thus distinction between classes would suffer.
I think this is not true, mainly because alchemy has a significantly lesser impact on the game than other skills, given the rarity of ingredients and because it is so difficult to train by a class that doesn't already have racial/class dice bonuses.
It could be one of the skills that don't reach 100 points even at PC level 50. Also, the effort required to get the skill and raise it to reasonable value would equal the effort of waiting for a RoDS to drop in TotHK cavernous levels and just wishing for the skill.
Also, alchemy's usefulness is somewhat random as the recipes may turn out to be simply not worth it. Vast majority of PCs would also never brew the PoGA until reaching D50 where it's welcome, but not particularly necessary.

Anyway, what do you think about this?