Interstellar Federations, Empires And Conflicts: Blish And Anderson

Star Trek has Klingons and Known Space has kzinti but let's just focus on James Blish and Poul Anderson.

Blish

In Cities In Flight, the Milky Way has four great civilizations:

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The Vegan Tyranny

The Earthman culture

The Web of Hercules

In "This Earth of Hours," the Terrestrial Matriarchy contacts and enters into conflict with the telepathic Central Empire.

A confederation at galactic centre is unnamed in The Star Dwellers, is called the Heart Stars in "A Dusk of Idols" and calls itself the Hegemony of Malis in Mission To The Heart Stars!

In "A Style in Treason," the Green Exarchy rules half of humanity's worlds and draws tithes from five fallen empires older than man.

Blish stated in private correspondence that interstellar distances were vast enough to allow such conflicts to remain unresolved.

Anderson

The earliest written part of the Technic History was a Captain Flandry story. Thus, the second major period of this future history is dominated by conflict between two rival imperialisms, Terra and Merseia, with Ythri as a third power. Terra has early border clashes with Ythri but permanent conflict with Merseia. 

Anderson's earlier Psychotechnic History begins with attempts to apply psychotechnic science to both society and psychobiology so it is appropriate that the interstellar rival of the later Stellar Union is a humanoid species whose science is biologically, not mechanically, based.