Jim picks up his briefing at a roller skating rink and is told about General Ernesto Neyron, a former dictator living in exile in Miami. He’s financing a military coup by cutting a deal with Frank Leyton, a Syndicate leader. In return for Syndicate backing, Neyron will give it exclusive gambling rights in his country.
Jim assembles the usual team and they go over Neyron’s mansion, and have replaced the man’s personal chef. Leyton works out of a Miami Beach hotel and they have a film prepared of Rollin disguised as Leyton. The film shows “Leyton” opening a safe, then turning and shooting the viewer. Cinnamon has a deck of cards that can be read from the back in the proper light, and Barney has a convex mirror set up to project a realistic image into thin air.
Neyron meets with Leyton to demand more money and Leyton chips in another half million. Jim goes to the hotel where Leyton is at and makes reservations for his secretive employer (disguised Rollin) for the top two floors.
Barney applies for the job of Neyron’s replacement cook and uses pre-cooked food to get the job, with Cinnamon and Willy as his assistants. They’re hired and Barney insists on their receiving quarters on site.
Jim inspects the hotel, drawing the attention of Leyton’s assistant. He then confronts the manager about the hotel’s business figures and demands a meeting with Leyton. In Neyron’s house, Cinnamon sneaks into his study and substitutes the special IMF cards.
Jim tries to buy the hotel from Leyton and when Leyton refuses, Jim threatens them with “outside pressure” and gives them 24 hours to decide. Barney works in the kitchen and starts cutting some onions to drive out the guard. Once he’s gone, they bring out the pre-cooked food they smuggled in and serve it as if they had cooked it. They then substitute one of their own fuses in the fuse box and rig the dumbwaiter that links the kitchen to the study so it holds their projector. While Willy runs their sound system into the house, Cinnamon draws a number on the table and tests their procedure for picking it up using a spray and adhesive paper. Barney is in there with her when Neyron’s man Colonel Santagura comes in and tells his men to inspect the kitchen… where Willy has the sound system still out in the open. Barney quickly keeps them out by claiming he has a soufflé cooking.
Leyton finds out that Rollin and Jim are running a scam to transfer their funds to the Caribbean, and that Rollin is a reclusive billionaire.
Leyton meets with Neyron for coffee and to receive his money after signing the Syndicate’s contract. He puts a copy in the safe as Barney secretly observes the combination. Neyron discovers Leyton is paying him in negotiable bonds and demands cash. Leyton warns he can’t get the money to him until the next day when the banks open, and Neyron holds onto the contract until the Syndicate pay off.
Rollin and Jim test an inflatable carryall that can look as if it’s fill and then not. At the mansion, Barney rigs the safe to open by remote. Cinnamon then uses the spray to pick up Neyron’s signature from the table.
Leyton sends a man in to bug Jim and Rollin’s apartment while Barney transfers Neyron’s signature to their own document. Jim finds the bug and then plays a radio to block it, while Barney injects an egg with a drug and serves it to him.
Jim goes to the bank early then returns to the hotel and gets in the elevator. Partway up he hides the expandable case in the roof panel then continues up to meet with Rollin. They stage a conversation for Leyton (listening in on the bug) about how they’re buying something other then the hotel, and he has an appointment later with their customer.
Neyron is taken ill from Barney’s drugged egg. Jim calls for a taxi and Leyton makes sure he ends up with one of his, while having Rollin watched. Barney takes Neyron’s order for supper while Willy secret plays a pre-recorded tape of Jim announcing a diagnosis. Barney pretends not to hear it and then they turn on the light overhead that illuminates the backs of the cards so that Neyron can see them. He displays his newfound knowledge to Barney, who again pleads ignorance. When Neyron calls in a guard, they turn off the secret light bulb so the man can’t see anything. Cinnamon then makes a call into the room and Barney pretends not to hear it again.
Jim leaves for his appointment while Rollin enters the elevator as Leyton’s man signals he’s coming down. Halfway down, Rollin shuts out the elevator and picks up the package Jim left earlier, then strips off his disguise and leaves while Leyton and his men wonder where the man went.
Cinnamon then makes another call to Neyron’s lounge, a “real” one this time. She informs him that Neyron’s doctor has decided to send a specialist. At the hotel, Rollin has his alter-ego paged. Jim arrives at Neyron’s mansion with Leyton’s man Grasnik following him to confirm he went in. Jim goes in with the case inflated then uninflates it once he’s inside. Rollin sneaks into Leyton’s office where Leyton’s men capture him at gunpoint.
Jim diagnoses Neyron with a rare syndrome and says the exact words Willy played early. Jim notes that the syndrome causes precognition and proscribes a tranquilizer, then tells the guards not to let Neyron be disturbed. Jim then switches bags and comes out, where Grasnik is waiting for him.
Rollin claims to be a Federal agent on the trail of his alter-ego, and says that they’re making a deal with Neyron. Grasnik comes in with Jim and reveals he’s made a deal with Neyron and shows them the contract with the forged signature. Rollin quickly grabs it and puts Jim under arrest. Leyton demands the return of his bonds but Rollin doesn’t care and suggests he go get the money himself.
After Jim’s drug injection, Neyron is increasingly dizzy and distracted, and the team set up the projector then play the sounds of approaching footsteps. They then run the projected footage of Leyton telling Neyron to open the safe and give him back his bonds. The projected image goes for the safe, which Barney opens on remote. He the goes for the safe, finds nothing, and turns and fires at Neyron. Neyron believes it’s another of his precognitive flashes.
Leyton pulls up to the mansion and Cinnamon lets him in to see Neyron. The situation pulls out the same way as the IMF’s projected hallucination and Barney opens the safe. When Leyton discovers there’s nothing there, Neyron pulls a gun and shoots him first. The team outside hears the gunshot and makes their exit as the police arrive.
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