Alter or Amend the Constitution. The constitution can only be changed via a Constitutional Amendment, which can be initiated by a State or by Congress, but must THEN have a two-thirds vote in Congress before going on to the States, at which point it must have three-fourths of the states agree on the proposed Amendment. In other words, the majority of elected Representatives at a Federal and State level must agree and pass the Amendment. So far, this has only happened 27 times.