If an alchemist takes 2 levels of rogue with the archetype underground chemist, does the archetype's special ability chemical weapons allow the rogue/alchemist to add his Intelligence modifier twice to the damage dealt by his bombs?
Controversially, the damage bonus from the creature's Intelligence modifier applies only once
The FAQ includes this exchange:
Question: Do ability modifiers from the same ability stack? For instance, can you add the same ability bonus on the same roll twice using two different effects that each add that same ability modifier?
Answer: No. An ability bonus, such as "Strength bonus", is considered to be the same source for the purpose of bonuses from the same source not stacking. However, you can still add, for instance “a deflection bonus equal to your Charisma modifier” and your Charisma modifier. For this purpose, however, the paladin's untyped "bonus equal to her Charisma bonus (if any) on all saving throws" from divine grace is considered to be the same as "Charisma bonus (if any)", and the same would be true for any other untyped "bonus equal to her [ability score] bonus" constructions.
an alchemist's bomb inflicts 1d6 points of fire damage + additional damage equal to the alchemist's Intelligence modifier
...and the underground chemist's class feature chemical weapons...
adds her Intelligence modifier to damage dealt with splash weapons, including any splash damage
...are both looking for the creature's Intelligence modifier to add it as an unnamed modifier to damage, so they wouldn't combine. However, were one or the other to grant a named bonus, they would combine.
When this ruling was made, there was grousing
I remember when this ruling was made, and there were at least a few threads devoted to its defense and destruction. A quick search only revealed this Pathfinder Society thread that seems rather indifferent about the whole thing (despite the thread's starter's obvious pleasure). That said, the Advanced Class Guide (Sept. 2014) was released almost concurrently with the ruling (Oct. 2014), so it might be the designers were wising up to this when the ACG was written, or, equally likely because of the way publishing works, that the ACG's designers anticipated and expected this interaction and found it unworthy of nerfing. So, in your home game if your alchemist is marginalized because of his insignificant bomb damage, you can point out the latter and ask the GM to let the Intelligence bonuses stack anyway.