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Hey there. I was wondering on something...
I like the idea of wizards and alchemists as classes, but would it be smart to multiclass them together? The reason why I ask is because
1) They're spellcasting classes
2) They rely on high Intelligence scores
My character that I'm suggesting this for is Vyranos himself.
No, because they have separate non-stacking casting.
For martial characters, multiclassing is less of a big deal, since BAB from Fighter stacks with BAB from Ranger. You still lose out on higher level abilities but its usually not too painful.
Being a caster is different. Having a 15th level character but only having 4th level spells sucks.
Unless you have something very specific you want from Alchemist levels, you'll be giving up a lot more by slowing down your Wizard spell progression than you'll gain by multiclassing. Spellcasters get most of their power from the highest level of spell that they can cast, so if you slow that down, you take a huge hit in power.
I have a Gestalted Wizard(Evocation)/Alchemist(Mindchemist and I Internal Alchemist Archetypes) and the two classes do dovetail amazingly well! But like the others have said, none of their abilities will increase through levels of the other.
An Alchemist with the Vivisectionist Archetype might be viable, if you plan on focusing on Ray Spells or Ranged/Melee Touch Spells, so you could tag on Sneak Attack damage to your magical firepower.
At the end of the day, whatever is the most fun to play, and that's the aim of the game.
Depending on the specific idea you have, it could work to a greater or lesser extent.
For a Arcane Trickster build, vivisectionist alchemist could provide the sneak attack pre-req instead of rogue.
Taking a single level of mindchemist alchemist for DC boosting cognatogen could work.
But, in general, mixing different casting classes just doesn't work.
Though there is the trick of going Sorc 1/Thassilonian Specialist wizard X so you can still use spell completion/trigger items as a sorcerer.
And of course, Sorc 1 (Crossblooded Orc/Draconic)/Evoker wizard for damage.
Wizard is a little forgiving since losing 1 level of casting still puts your access to spell level equal to a sorcerer.
I've always loved the idea of multiclassing Wizard and Alchmist. So, I'll suggest a couple options, which will depend on what sort of Wiz/Alc combination you are looking for.
1) There is the wizard's Arcane Bomber archetype.
2) If you were really set on multiclassing, you may want to check these out. Hopefully these will provide you with an appropriate option for your character.
Esoteric Chemist (Wiz/Alc - Extracts)
Incendiary Mage (Wiz/Alc - Bombs)
Or, your can always build your own HERE.