Similar, but Different, Class Abilities Stacking?

[Zahir ibn Mahmoud ibn Jothan]

I'll give an example, but there are lots to choose from.

Pathfinder Chronicler has some abilities that stack with Bard abilities, Bardic Knowledge, and Performance.

How does this stacking work with non-canonical versions of those abilities from other classes or archetypes? For example, the Dervish Dancer's alternate performances?

Feel free to pose other examples of this.

[Zahir ibn Mahmoud ibn Jothan]

No takers on this question, which is vital to the defense of Magnimar?

[wraithstrike]

If an archetype trades an ability out then it wont stack unless the new ability specifically says it work as or counts as the old ability.

[wraithstrike]

I forgot to add sometimes an ability will specifically be a variant of the base ability. The fighter archetypes do this sometimes. Those would also count.