There are multiple ways for parahuman, non-human or group to be labelled a class-S threat.
High level duplicators and villains who operate to any exponential degree are automatically considered S-class if their powers generate more instances of power generation or recurring effect in an epidemic pattern.
Three PRT Thinkers must all rate a situation sufficiently highly before it can be considered an S-class situation.
Being labelled a class-S threat is equivalent to kill order, in addition to which the PRT calls everyone they can to destroy the threat. According to Miss Militia, the difference in response to a class A crisis and a class S one is minor. Some tertiary protocols change, the Triumvirate are guaranteed to assist, and there are penalties for anyone who subscribed to the critical situation roster if they sit it out.
There are epidemic protocols for dealing with a Class S situation.
The above emerged as class S threats over the course of the story. Further, Ash Beast has the potential of being an S-class threat but moves slowly enough to be avoidable, and Blasto had a "high risk" of becoming S-class.
There were threats of a similar level that were not widely known, and were dealt with by organisations such as the Thanda. Some tinkers (Bonesaw, Rattenfänger, Jamestowner, Mosaic, Monstrum) and other capes like Chrysalis have the potential for becoming S-class threats, if they could find some outside means for cooperation or a power boost/second trigger.
↑Take stock. Who didn’t I have? I didn’t have Contessa, who I couldn’t see. I didn’t have the Blasphemies, who hadn’t even registered to me because they weren’t human, even if they had powers, I didn’t have Sleeper and… - Excerpt from Speck 30.5
↑Keep in mind that S-class threats can include groups, as it does with the S9. - Wildbow on Reddit
↑The self-recursive thing is a definition of an S-class threat, but not the definition. - Wildbow on Reddit
↑“We’re talking class-S, even if you ignore pre-situation verification. Section nine-seven-five, article fifty-seven. Classifying high level duplicators and villains who operate to any exponential degree. Nilbog and Simurgh both count, and Noelle does too. If the powers generate more instances of power generation or recurring effect in an epidemic pattern…” - Exerpt from Queen 18.4
↑“Bullshit,” Tattletale said. “S-class. I know Appraiser offered a purple-velvet diagnosis for his previous ratings on Endbringer attacks, so that’s not the reason it’s so low. Eleven’s score of eight has to be above the seventy-five percent mark, and an answer as vague as Hunch’s is going to be a seventy-five percent exact, as per section nine-seven-six, article seventy-one. That’s three values that have to be above the threshold for declaring a threat level S situation.” - Exerpt from Queen 18.4
↑To be clear, the self-reproducing creations thing is what gets you labeled as a Class-S threat. That's basically a kill order, but more in the line of "We're going to call in everyone we can to put you down." - Wildbow on MythWeavers
↑“I don’t know why we’re even discussing this, when you seem to have our operations manual memorized and you’re capable of realizing it for yourself,” Miss Militia said, “but it doesn’t bear dwelling on. The difference in our response to a class A crisis and a class S one is minor at best. Some tertiary protocols change, we won’t necessarily have Alexandria, Legend or Eidolon assisting, and there’s no penalties for anyone who subscribed to the critical situation roster if they sit this one out.” - Exerpt from Queen 18.4
↑“If the heroes aren’t showing in full force, others won’t either.” Tattletale said, “And there’s no epidemic protocols with a class-A.” - Exerpt from Queen 18.4
↑ 9.09.19.29.39.4There’s six class S threats active in the world at large. The Endbringers make up three of them. The Slaughterhouse Nine as a group are a fourth. - Exerpt from Queen 18.3
↑ 10.010.1Week I had clearance, I watched all the video we have of the class S threats. Leviathan, Simurgh, Behemoth, Slaughterhouse Nine, Nilbog, Sleeper. - Exerpt from Queen 18.4
↑I reached out to Ash Beast, a living force of nature. It had originally triggered in Matruh, Egypt, and had been roaming since, making its way across Africa. All of the destructive power of any class S threat, tempered by the fact that it usually traveled on foot, and people could see it coming from miles away. When it reached a settlement, that settlement was usually evacuated. - Exerpt from Speck 30.5
↑[The Thanda fight] the class-S threats that aren't so obvious as Sleeper, Nilbog or the Blasphemies, and the villains who don't take the spotlight. [...] Perhaps it would be better to say Class-S level? Not necessarily known & classified, but arguably as dangerous in their own right? - Wildbow on Spacebattles
↑“Someone’s doing their level best to make their own Endbringer.”
“Yes. There’s also any number of megalomaniac tinkers out there who might have tried something. Bonesaw, Rattenfänger, Jamestowner, Blasto, Mosaic, Monstrum, some non-tinkers like Chrysalis and Nilbog, bunch of others.” - Exerpt from Queen 18.1
↑They're explicitly stated as not being strong enough, but the theory goes that they could find some outside means for cooperation or a power boost/second trigger. - Wildbow on RPG.net
↑Trickster - Line of sight, swaps everyone and everything, comingles swapped matter - person + mailbox = two mashed together abominations of flesh and mailbox, slowly dying as organs fail. PRT van + PRT van = two mashed together heaps of metal with people crushed inside, very possibly setting fire or exploding given friction of metal on metal and leaking gasoline. Size/mass/density sense that normally allows Trickster to gauge how swappable things are is extended to give knowledge of everyone and everything within a one-mile radius. Reflexes amped up. Effectively navigates a battlefield by swapping himself instantly and repeatedly, mapping out routes in advance, leaving mangled destruction in his wake, flanking and hiding. - Wildbow on Reddit