Double Jeopardy in the U.S. does have some exceptions to it, and this might not be impermissible in the United State. There's generally three exceptions, and I'll discuss from most common to least common. First, I'd like to clarify two things:
For my discussions the term "Event" will be used to indicate a specific alleged crime and will be specifically original with respect to alleged perpetrator, victim, and time, manner, and place involved in the crime.
In the U.S., Double Jeopardy is often best understood as a ban on the prosecution (state) from initiating the appellant process. They can only appeal subsequent decisions after the defendant appeals the initial case. The defendant will appeal a decision if they are found guilty, but would never appeal an acquittal. Since the prosecution cannot initiate appeals, the only time they will happen is following a guilty verdict. Double Jeopardy is also specific to one event. If Alice is acquitted of a charge of Murder for killing Bob, she cannot be tried for the murder of Bob ever again. She can still be prosecuted on a charge of Murder for killing Charlie as the two events are separate (by dint of the fact that the victims are different) and for perjury if she testified falsely to her innocence in killing Bob (i.e. new evidence brought to light would have convicted her after the fact). This is also a seperate event as the new trial is about whether she lied while under oath, not if she killed Bob.
That out of the way, in the U.S. there are three general exceptions:
- Dual Sovereignty - Double Jeopardy only applies to a single court system, while all U.S. citizens are under at least 2 court systems jurisdictions at any time: Their State (or territorial) and the Federal Government while in U.S. Geographic Territory (and Embassies and overseas holdings). Typically the states prosecute most crimes first and the Feds will prosecute any related crimes second. If it's between two or more states, the Feds and all states party to the crime will have to negotiate, though typically the feds will defer to states first. If a state and the federal government have the same law, the feds may prosecute for the exact same crime regardless of outcome.
For example, suppose a man illegally crosses the Canadian Border into Montana and kills someone. The state of Montana can prosecute the illegal immigrant for murder and the U.S. federal government can prosecute him for both Murder and Illegal immigration. In practice, however, the Federal Government usually will respect the outcome of the state's case for all similar crimes so the defendant could be acquitted of Murder in Montana, and the Federal Government will likely drop the charge and just try him for illegal immigration (a strictly federal crime). There are some situations where the feds will try the murder despite the conviction, but it's usually if federal prosecuters think that some shenanigans were involved. At the absolute worst, as many as 7 seperate courts could have jurisdiction on one event (If you commit a crime at the Four Corners (the border between Colorodo, Utah, Arizona, and New Mexico, the only place in the U.S. where four states share a border) in addition to the Federal Government and two Tribal governments (the Utes in Utah and the Navajo in the other three all have reservation jurisdiction at this point. In the case of the Navajo, they only have one reservation in the three states, so they don't get three seperate cracks at it.).
Directed Verdict - Less likely, but still a possibility, Directed Verdict occurs when a Judge tells the jury to render a verdict for a charge. If this occurs, it will be immediately after the Prosectuion resting their case and before the Defense calls their witnesses. The Defense is entitled to make a motion for dismissal of charges and if granted, the Judge will instruct the Jury to find "Not Guilty" for at least one charge if not all of them. Basically, they are granted if the Prosecution fails to even meet evidence burden of the charges that he grants. It's actually quite common to make the motion, though it is rare to have it granted. The Judge may also consider making the grant after closing remarks before giving the case to the jury for deliberation. If it is granted, the Prosection will be given the right to appeal the verdict. If you'd like to look up some cases, the directed verdict was granted to some charges in one of the Freddy Grey Murder trials (I forget which of the defendants got it, but it wasn't appealed as the rest of the charges were found "Not Guilty") and a Defimation case against Project Veritas (though this was a civil case, the judge felt the elements of Defimation were not met by the prosection to sufficently even let the jury decide. The Plaintiff may start appeals in Civil cases, so Double Jeopardy is not a thing. One of the Defendants has a description of the experience on their Youtube Channel if you would like to learn more about the case).
Fixing the Trial - If it can be proven that some of the jury or the judge in a bench trial were unfairly biased to the Defendant through means outside of the court and acquitted the defendant, then the defendant was never "in danger of life or limb" to quote the Constitution, and thus, a second trial on the same event is not a violation of Double Jeopardy because they weren't in Jeopardy the first time. This has happened exactly once in all of U.S. History (a member of the Chicago Mob was given a bench trial and the judge was bribed to find the defendant "not guilty." The Judge eventually confessed to this in his suicide note and the courts ruled that jury or judge tampering to be an exception to Double Jeopardy with respect to the original trial. The mobster was tried for the exact same event in the exact same court twice and found Guilty, the only time this has ever occurred in U.S. History.).
It should be pointed out that mistrials and new trials granted on appeal are not exceptions as in both instances, the legal fiction in place is that the original trial never happened and the Defendant is being tried for the first time. Mistrials can be declared prior to the verdict by anyone, but only by request of the Defense on appeals, and new trials are always granted by the defense on appeal. The Prosecution has to recharge the defense with the crime and may choose not to for any number of reasons (from the case was weak and barely got the guilty verdict to losing evidence critical to securing a new guilty verdict to the recovery of exculpatory evidence that proves the Defense was innocent all along.).