[finn]

Sounds like a form of Extra Attack, with limitation of "Only right after a successful attack within the same turn" and "only against a enemy not attacked within this 'chain' "

The first limitation should get progressively larger for the 3rd, 4th, and 5th attack. This is because the 3rd, 4th, and 5th attack each require that each and every attack before them to be successful.

The second limitation should get progressively larger too, as there will be a smaller pool of enemies to choose from as the number of 'chain' increases.

Maybe you could add the two limitation together and call it a -50% limitation for the first Extra Attack (the 2nd attack in the chain), -60% for the second, -70% for the third and so on.

Note that you might need the +20% enhancement to use the same weapon multiple times in the chain. If the Extra Attack can only be used for a specific Innate Attack, that should be a limitation too.