Along the lines of "Lost the RPG", here's an adaptation of another TV series with Terry O'Quinn in a major role: Millennium, the series about a group that appears at first to merely be consulting on serial murder cases, but turns out to be an ancient conspiracy obsessed with a coming apocalypse. Again, use either JAGS Wonderland or port it to InSpectres (or some other system.) If you are using InSpectres, you should probably use the "multiple franchises" rule I described before. If using JAGS or another build-points game, you buy a relationship or other link to a group.
Characters start in a law enforcement franchise of some kind, with no dice/points invested in the Millennium Group. They can be either uninfected or have low Unsanity. However, they usually have some minor talent similar to magic: they can catch glimpses of things on lower chessboards, or get warnings from a "guardian angel". This is what interests Millennium in the characters and triggers contact.
Characters investigate mysteries -- crimes, usually, and often violent ones -- on Chessboard 0. At first, they use their gift (and, eventually, physical resources of Millennium) for insight into horrific but otherwise mundane Chessboard 0 events. Millennium seems like just an ordinary group with extraordinary resources and a belief that the world is really getting worse, so someone needs to stop things from getting worse.
Many of the mysteries being investigated are being influenced by reflections on Chessboard 0 of things from a far deeper level. After solving several mysteries, the characters will begin to encounter these beings directly, always mistaking them for ordinary serial killers or corrupt officials (The Judge, Lucy Butler, Mabius, and other instruments of the demon Legion.) These beings can perform limited breeches of natural law and thus will usually lead to infection or trigger episodes, sending characters down to Chessboard 1.
However, in addition to individual mysteries, there's a big meta-mystery, the Conspiracy. The real explanation of what Millennium is up to. This is tracked with a separate Conspiracy score that starts at 0 points (or dice, in InSpectres terms.) Although mundane mysteries and even mundane conspiracies can be solved on Chessboard 0, the big Conspiracy can only be solved by having episodes. Investigating Millennium on Chessboard 0 results in inexplicable discoveries; investigating on a lower chessboard earns points/dice to add to the Conspiracy score. When it reaches a GM-determined level (usually 10,) the Conspiracy is mostly solved.
Episodes are limited to Chessboard 1 until the Conspiracy rating rises. In general, characters can descend one chessboard deeper every time the Conspiracy rating doubles. The deeper the episode, the shorter it lasts; Millennium focuses mainly on the effects of the deeper levels on Chessboard 0.
Once Conspiracy reaches 1, characters will notice that fully-made Millennium members have more control over episodes than most infected. They all have at least Advanced levels of Mastery, up to full Master level for characters like The Old Man. They also have access to "magic" based on shadow control, generally expressed as prophetic knowledge, clairvoyance, or seeming control over coincidence and probability (witness the "accident" that kills Frank Black's friend from The Trust, or Lara Mean's obsession with rolling dice when she becomes a full member.)
As Conspiracy rises, characters will become aware of factions within Millennium (Owls versus Roosters, for example,) schisms (The Family,) and rivals (Odessa.) The game will change from simple criminal investigation to a war over the future of mankind.