Thanks to the existence of Plot Tokens, every star is a potential equal in the plot of the story regardless of the potential power of the characters. This makes SOAP attractive if one wants to play a game where vast differences in power level are possible, such as a lot of comic books and superhero settings. In the incredibly soapy Lois and Clark TV show, for instance, both Lois Lane and Clark Kent are of equal importance to the stories being told, despite only one of them being able to bounce bullets off his chest.
In order to fully emulate the superhero genre, however, some rules additions must be made.
These rules additions work well in many genres - I've used the Secret Identity to great effect in a horror game, with a werewolf.
A star may choose to have a secret identity (he doesn't have to); this must be decided during character creation or character advancement. Stars with secret identities may pick two sets of Traits, one per identity, as well as having different Home Sets and two sets of Relationships. This helps to separate the two personae. Character attributes common to both identities may be taken twice, but otherwise the star may only collect Plot Tokens for those attributes appropriate to his current identity. Switching identities off-screen takes no time. Switching identities on-screen requires a sentence, but gives the character a Plot Token for his effort. A character's identity is also protected from discovery by other characters as if it were their Home Set.
Why not just use the Secret rule for this? Because you want to be able to show the contrasts in the Secret Identity on the screen. To put more simply, it's more enjoyable to watch both Clark Kent and Superman than it is to just watch Superman. At least, it is for me. If your secret identity is your Secret, then you can't write a sentence where Clark Kent runs towards that phone booth, pulling apart his shirt to reveal the S underneath. You wouldn't be able to see Norman Osborne and Peter Parker growing closer while Spiderman and Green Goblin tear up the streets with their enmity. In other words, it goes against genre.
The other nice thing about the Secret Identity rules as written is that they ensure your character will never be in two scenes at the same time, once in their normal ID and once in their super ID. Oh yes, by the way, if someone really want to have more than two lives to juggle, they can take additional identities. The only limitations are realism and sanity. Mystique, for instance, likely has a number of Secret Identities she keeps up (and likely adds more through play, which simply takes a sentence and a Plot Token, but can be contested). This is definitely a situation where the players all know, but the characters shouldn't.
A Secret Identity acts like a Home Set for the purpose of resisting discovery; thus if another player narrates the Secret Identity being discovered by an individual, it is easier to contest. In addition, discovery is often only temporary; any sentence that negates the discovery somehow (mind-wiping, evidence to the contrary, etc) can be defended. This is for any discovery.
Of course, there's nothing stopping you from using a Secret for your Secret ID, if you want to play that way. In that case, the name of the extra who is your "normal" form (or in rare instances, your "super" form) must be one or more of your Secret Words, and you can be killed once "exposed."
If a character has superpowers, it is important to know what those powers are. But those powers should not generally fill up a star's Background, taking space away from more personality-focused Traits, because that would lead to a character with only one dimension instead of two, which would make the audience less likely to care about him, either sympathetically or viscerally.
So, after selecting Traits and before selecting a Secret, the player may describe the character's superpowers, which we shall call his Schtick. Spiderman would thus have a Schtick mentioning his wall-crawling, spider-sense, strength, speed and webbing. Superman would mention his x-ray and heat vision, his superbreath, his strength, his flight, his bullet-bouncing and so on. People without powers would skip this step entirely. There is no limitation to what powers a character can have - Plot Tokens are the true power in the game, and in that way all characters are on equal footing.
Special Effects aren't cheap! Whenever a Schtick is used in a sentence on-screen, the author of that sentence must pay a Plot Token for the special effects budget. This is regardless of how many powers come into play. Note that a specific power may also be one of a star's five Traits, in which case it's not considered part of the Schtick, and the character does not get charged for its use.
Whenever an extra comes on screen for the first time, the author may define that extra's Schtick for free, adding as many or as few powers as desired. That definition comes hand-in-hand with the extra's appearance, so if another character contests and wins, they gain control over the Schtick as well. Any character's Schtick may be changed at any time; this must happen simultaneously with a sentence that displays the change and costs one Plot Token whether it succeeds or fails. As with everything else, schtick changes should make sense within the story.
Any time a star writes a sentence that contradicts a defined Schtick of a character (like having a superstrong character bested in arm-wrestling by a weakling) and there is no Schtick being defined to explain it, that Schtick acts as a Home Set. Even if no one contests it, the author must still put up at least one Plot Token in addition to any SFX charges.
Many superheroes have weaknesses, fatal flaws or Achilles heels. By far the most well-known example is Superman and kryptonite, but there are many others, often not nearly so direct. A weakness can be anything - Professor X is bound to a wheelchair; Cyclops can never turn off his laser vision; the Hulk's weakness is stupidity while Bruce Banner's weakness is involuntary change; Nightcrawler looks freakish, causing people to run away; and any number of superheroes have a Weakness in the form of "threats against those I care about." Anything can be a weakness - codes of honor, addictions, dependents, or even just a bad reputation.
Whenever someone uses a character's weakness against a character in a sentence, they are considered to be on their Home Set (this is cumulative with the actual Home Set advantage). So, why would you want a weakness at all? Because whenever that happens, after the dust has settled, you get a Plot Token for your troubles. You also get a Plot Token whenever you inflict your weakness on yourself in a story-appropriate manner.
Note that many characters have multiple weaknesses.
Nobody Dies Except Bucky
In many comic books, nobody is ever dead for good, and this can be reflected in gameplay. This is excruciatingly simple - just skip the Secret step of character creation entirely. To balance out the lack of secret words and the potential to gather Tokens with them, when using these rules every Trait gives two Plot Tokens instead of one (Relationships continue to give only one Token). True death is now impossible, at least for the stars, unless they choose to narrate it themselves.