The ten amendments that form the Bill of Rights are often treated as part of the original Constitution, being almost contemporaneous with the original text and having been written by the prime architect of the Constitution, James Madison.
Subsequent amendments fall into a different category. They are fixes to flaws in the original text. Some of the flaws were made apparent by the operation of the government the Constitution created. Others were flaws revealed by changing ideas of what government ought to do.
The Eleventh Amendment arose from a lawsuit brought in federal court by a South Carolina merchant named Alexander Chisholm against the state of Georgia for payment of debt. The verdict in favor of Chisholm was less important than the fact that the Supreme Court upheld Chisholm’s right to use the federal courts to sue across state lines. The court cited Article III of the Constitution, which gave the Supreme Court original jurisdiction in any suit “between a state and citizens of another state.”
The many lawyers at the Philadelphia convention failed to appreciate how much the states would resent this threat to the principle of sovereign immunity, which prevents most lawsuits against governments for actions taken in the ordinary course of government business. Without it, governments might be buried in lawsuits. Georgia courts protected Georgia’s government, but Article III opened Georgia to Chisholm’s suit in federal court.
As soon as the Chisholm decision came down, the states almost as one demanded a fix. Congress responded with the Eleventh Amendment, which read, “The judicial power of the United States shall not be construed to extend to any suit in law or equity commenced or prosecuted against one of the United States by citizens of another state, or by citizens or subjects of any foreign state.”
The amendment was referred to the states. The requisite three-quarters of them ratified by early 1795. Loophole closed. Sovereignty immunity restored.
The Twelfth Amendment arose from an even more embarrassing snafu. America’s first two presidential elections were essentially uncontested coronations of George Washington. The third election, in 1796, was the first contested election and the first in which political parties played an important part. Federalist John Adams narrowly defeated Republican Thomas Jefferson. Because the Constitution had been written without parties in mind, the framers supposed that the runner-up would be the most suitable substitute should the president die in office. In fact the runner-up was the worst substitute, or nearly so, given that his partisan agenda would be the opposite of the winner’s. If Adams had died in office, the executive branch would have swung from ardent Federalist to devoted Republican.
This by itself might have occasioned a rewrite of the rules for electing presidents. But the election of 1800 revealed another problem with that part of Article II. Each of the Republican electors cast one of his two ballots for Jefferson and the other for Aaron Burr of New York. Burr was understood to be Jefferson’s understudy, but the tie threw the race into the House of Representatives, where the departing—because rejected at the polls—Federalist majority could determine which of the Republicans became president. The temptation to mischief was overwhelming. Some Federalists sought to make Burr president in exchange for promises of favors from him. Nothing came of the efforts except bad blood between Burr and Hamilton, the latter of whom persuaded Federalists in the House that Burr was evil while Jefferson was merely misguided. Jefferson became president, and nearly everyone decided that the system for electing presidents had to change.
The crucial revision was that while each elector would still have two ballots, one would be cast explicitly for president and the other for vice president. This would prevent a repeat of the Jefferson-Burr confusion.
Of no less importance, this change informally wrote parties into the Constitution. The Twelfth Amendment didn’t use that word, nor faction or other synonym. But the new structure of electoral voting was based on the premise that presidential candidates and vice presidential candidates would run as pairs—members of the same party.
No longer would the vice president be the disappointed runner-up, a man tempted to conspire against the president, as Jefferson did against Adams. No longer might the death of a president produce a dramatic swing in administration policy. The swing from Adams to Jefferson upon the latter’s 1801 inauguration was certainly dramatic, so dramatic that Jefferson called it the “revolution of 1800.” Yet it was a revolution mandated by voters in the 1800 elections. Had Adams died in office, the revolution might have been just as dramatic, but it would have been less convincing.

Excellent breakdown of how actual governance exposed constitutional gaps. The Burr situaton really highlights how the framers overestimated institutional norms. Once parties emerged, assuming the VP would be a loyal backup turned out to be naively optimistic and I've seen how institutional design fails without accounting for coalition behavior.