Does the knife master ability stack with prestige classes?

Question

I'm making a villain for a campaign, and he's going to be an assassin/rogue combo. I wanted him to have a bit more bite, though, so I decided to make him a knife master.

Would the sneak stab ability that the knife master rogue archetype gives change the sneak attack damage from the levels of assassin as well, or would that damage remain d6s while the rogue-levels sneak attack deals d8s/d4s?

EDIT: Sneak Stab wording;

A knife master focuses her ability to deal sneak attack damage with daggers and similar weapons to such a degree that she can deal more sneak attack damage with those weapons at the expense of sneak attacks with other weapons. When she makes a sneak attack with a dagger, kerambit, kukri, punching daggers, starknife, or swordbreaker dagger, she uses d8s to roll sneak attack damage instead of d6s. For sneak attacks with all other weapons, she uses d4s instead of d6s. This ability is identical in all other ways to sneak attack, and supplements that ability.

Answer 1

It does say “when she uses Sneak Attack” and that this ability “supplements” that ability. I would argue that it applies to all abilities named Sneak Attack – the Knife Master doesn’t really gain a different form of precision damage that’s similar-to-but-distinct-from Sneak Attack, she gains an ability that modifies Sneak Attack. It would apply to all Sneak Attack that she has.

Certainly, from a balance/ease-of-play/flavor sense, it should apply.