Sabalom Glitz suggested that he could sell secrets from the Matrix to "a government here, a federation there." (TV: The Mysterious Planet)
In N-Space, there existed the American Federation of Musicians, (PROSE: Atom Bomb Blues) Earthlink Federation, (PROSE: The Gods of the Underworld) Federation of Three Worlds, (TV: Snakedance) Federation of Worlds, (COMIC: Kane's Story, Frobisher's Story) Galactic Federation, (TV: The Curse of Peladon, The Monster of Peladon, et al) Shadow Federation, (PROSE: The Gods of the Underworld) and the Terran Federation. (COMIC: Pureblood)
In a parallel universe, there existed the United Federation of Planets. (COMIC: Assimilation²)
Behind the scenes
The Terrestrial Index, which dated the events of Snakedance to the 31st century, identified the Federation system as a local federation which preceded the establishment of the Galactic Federation by the 32nd century.