I certainly don't want to sound like a ____ but this is incorrect. You absolutely can't retry a person for the same "incident" once the first witness is sworn in. Prior to the first witness if the perp confesses to additional crimes or new evidence comes to light yes, after the trial effectively begins it's a wrap. The government is allowed 1 prosecution per "crime". If you kill someone and you are prosecuted for breaking and entering and the trial begins you can not be charged with murder as that is literally the definition of double jeopardy (subject to loss of freedom more than once for the same incident).
See below especially the bolded sections for clarity on this.
The U.S. Supreme Court curbed this discretion in Blockburger v. United States, 284 U.S. 299, 52 S. Ct. 180, 76 L. Ed. 306(1932), in which it wrote that the government may prosecute an individual for more than one offense stemming from a single course of conduct only when each offense requires proof of a fact that the other offenses do not require. Blockburger requires courts to examine the elements of each offense as they are delineated by statute, without regard to the actual evidence that will be introduced at trial. The prosecution has the burden of demonstrating that within a pair or group of offenses, each has at least one mutually exclusive element. If any one offense is wholly subsumed by another, such as a lesser included offense, the two offenses are deemed to be the same, and punishment is allowed for only one.