Do note that there can only exist two types of incinerate: A normal one (can be modified) and a custom one. That's why there are only two types of it in DotA (
Fury Swipes which just adds damage each attack
and Caustic Finale which just explodes upon death). You can know that they are based off this ability because they don't leave corpses.
Of course you can trigger the whole effect, which I think DotA has already done since the various modifications to the abilities have taken place. It will also allow you to keep more than two "Incinerate" type abilities.
Though it is just a rumour I have heard several times from advanced coders (which have association with DotA), I'm not a 100% sure this is true.
EDIT:
Ah, after googling it a little more, here is what I have found (taken from playdota):
Fury Swipes is [ANic] Incinerate. Incinerate-based abilities with a different ID don't deal bonus damage (the explosion works though).
So basically, Fury Swipes is just a modified
non-custom incinerate because the custom ones don't deal bonus damage. This means that there can be lots of different incinerate type abilities, but only one of them will be able to deal bonus damage.