I've been looking into playing someone that makes a lot of alchemy items for a current game, and started wondering.
What are all the ways I can increase the DCs of Alchemical items in D&D 3.X and Pathfinder?
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You can use the Full Pouch spell which creates a duplicate of another alchemical item. The interesting part being :
Saves against the new alchemical item’s affects use the original item’s save DC or the save DC of this spell, whichever is higher.
By increasing the DC of this spell you can create an alchemical item with a higher DC than the usual.
In theory you could try to reduce the cost of such a process by using the spell directly on an already duplicated item. However, the spell explicitly states :
You cast this spell as you draw out a consumable alchemical item to use.
The (probably dangerous) consequences of using this spell without using the duplicated item thereafter should be decided by your GM.
You can throw a single alchemical item as a full-attack action, increasing the effectiveness of the alchemical agent thrown. When throwing a single alchemical item as a full-attack action, you increase the DC of any effects associated with that alchemical item by 2. When your base attack bonus reaches +11 and every 5 points of bonus thereafter, increase the saving throw DC of the alchemical item by an additional 2. This feat does not apply to an alchemist’s bombs.
Notably this seems to stack with the spell mentioned in @Rophe's answer, making it a potentially powerful (whereas otherwise it's only moderately useful).
It's notable that this is not an uncommon question, and it clearly has very few answers.