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After pulling it off, they learn that they were hired under false pretenses—they don't get paid, or their employer isn't who they thought, or the justification they were given for the theft turns out to be a lie.
They then pull another iteration of The Caper on their original employer, for vengeance and/or to get the stolen goods back to their rightful owner.
This is often used as a way to have a plot based on The Caper that has some degree of moral justifiability. It also provides a built-in structure for Up to Eleven in the execution of Caper #2.
In X-Men Noir: Mark of Cain, Thomas Halloway and his ersatz X-Men (Cyclops, Captain Logan, and Eugene Judd) are hired by Halloway's old father figure Cain Marko to steal the Crimson Gem of Cyttorak from a temple in Madripoor. When they deliver the gem, Marko double crosses them; he paid them in newspaper. They don't go after Marko — because someone beat them to it. They decide to track down Marko's killer instead, reasoning that whoever did him in must now have the gem.
The team in Sneakers is hired to steal an encryption device from a mathematician. Their employers claim to be NSA agents, and say that the mathematician is being funded by Russia. Actually, he's being funded by the NSA, and the employers work for The Syndicate.
The remake of The Italian Job has the crew pulling a caper against the guy who double-crossed them and took the gold from their original caper.
While not a clear example of a caper, Dirty Work starring Norm MacDonald has Christopher McDonald's character hire the protagonists to vandalize an apartment building he claims belongs to him and is actually a brothel. After this, they find out that another man owns the building, and the person they thought was the "Madam" was just a sweet old lady with a knitting circle. The bad guy just wanted to have the building condemned and leveled, so he could get the land. Naturally, they stage a comeback to expose the guy and get him to pay for the damages.
The Jeffrey Archer book Not A Penny More, Not A Penny Less is about a stock market fraud and the subsequent attempts of the defrauded parties to steal back the exact amount they were scammed out of. At the end the originally worthless oil company stocks are suddenly valuable — after an oil strike nearby — and they have to find a way to run the whole theft in reverse to return the money.
The pilot of Leverage, "The Nigerian Job", has a team of thieves hired to steal a set of airplane plans from a rival aerospace corporation. They're told that the rival corporation stole the plans first. Then their employer doesn't pay them and tries to kill them, and they learn that he'd lied and they'd stolen the plans from the rightful owners. Counter-caper time.