Why wouldn't you? Mutagen is an alchemical bonus, rage is a morale.
I agree with MrSin. The name of the bonues i.e. alchemical,morale,luck,enchancement,etc. just has to be different in order for them to stack.
You both misunderstand, Mark is referring to the ragechemist's ragemutagen.
But yes, they both stack. You gain ragemutagen's effect whenever you use a str mutagen and you gain feral mutagens effect whenever you use a mutagen.
But personally I don't like the ragechemist, if take too much damage, you could fall into a coma during battle. If you want to become more like a monster, I would suggest looking into the beastmorph archetype.
I played a similar character in PFS. Some of the feats/discoveries I took are feral mutagen, spontaneous healing, healing touch,preserve organs, mummification, wings, fast bombs, force bombs, power attack and lingering spirit. With all that, he is pretty hard to kill.
Also, at lv 10 the beastmorph archetype can give you pounce, among other monster abilities.
Oh! I see now. Yes, Rage Chemist augments your mutagen. Its technically still a mutagen, just with all of the changes listed on rage mutagen. Any discovery that changes your mutagen still affects it, no change there.