At a standard windward starting line with all boats on starboard tack,
W is early at the starboard end and reaches down below the line
making contact with two leeward boats before tangling briefly with a third leeward boat.
No serious damage results.
RRS 41.1 says "A boat may take... a penalty when she [has] broken one or more rules... in an incident..."
All three leeward boats hail protest.
How many incidents have occurred, and thus how many turns does W owe?
After the first contact she did not get well clear of other boats as soon as possible, so any turns she takes are not a Turns Penalty in accordance with RRS 44.2.
I think each contact is evidence of a separate breach of RRS 11 and RRS 14, so that's 3 incidents.
US Sailing Appeal 65
The test of whether two occurrences were one or two incidents is whether the second occurrence was the inevitable result of the first. A boat intending to protest another boat for two incidents during a race, no matter how close in time, must inform the protested boat that two protests will be lodged.
RYA Appeal 2003/3
If there is a causal link between a series of collisions, they may be regarded as a single incident for the purposes of rule 60.3(a)(1).
The second contact was not caused by or a result of the first.
The third contact was not caused by or a result of either the first or the second.
So no link or consequence there.
In accordance with Case 49 protests for all the incidents should be heard together.
If she did turns, that may satisfy 1, but 2+3 can protest her and argue either side in the jury room. Or, it might satisfy 3, and 1+2 might protest.
This is not a unique scenario. P (port) sails across S1 (starboard) bow forcing her to take vaping action. P continues for 2 boat lengths while S1 expresses her intent to protest and P replies with some words of defence ("sorry"). Hasn't initiated turns but is now repeating the process for S2.
The quoted US situation -- actually refers to the same boat making the protest. Perhaps P avoid S2 but infringes S1 again.
And OP - for me, there appear to be 3 incidents here as per the independence criteria.