Third way is essentially a rightwing capitalist think tank posing as progressive. They, along with Bill Clinton and his DLC started the party shift to the right to in order to appeal to big money that had normally been flowing to republicans. They are opposed to third parties because it would harm capital.

Their name Third Way doesnt imply an an alternative approach to government, but representative of triangulation, the centrist approach to government, a little leftish a little rightish