Comment by smacktoward

Some political scientists would say we're actually on our third or fourth.

The third U.S. republic was created after the Civil War, with the passage of Constitutional amendments that made the Federal government unambiguously superior in power to the governments of the states.

The fourth U.S. republic was created during the Progressive Era, with the creation of the "regulatory state" in which significant authority over economic matters was delegated from Congress and the courts to regulatory agencies in the Executive Branch. This system evolved gradually over the years (with the biggest changes coming through Roosevelt's New Deal and Johnson's Great Society) into the system we live in today.

The changes wrought by the Civil War were unfortunately quite violent, but all the other changes have been peaceful, as you note. Our ability to reinvent our democracy in this fashion is a big part of why the Constitution has survived so long -- we can change how we govern ourselves in big ways without having to tear it up and start anew.