War World I: The Burning Eye, which contains stories by Poul Anderson, SM Stirling and Harry Turtledove, has been ordered and should arrive soon.
Anderson's Technic History has:
civil wars in the Polesotechnic League and the Terran Empire;
a war between the Terran Empire and the Domain of Ythri;
several battles between Terrans and Merseians;
but a lot more going on than wars and battles.
Larry Niven's Known Space future history has a period of wars between men and kzinti but a lot more going on. Jerry Pournelle's CoDominium future history is a succession of war periods diversified only by alien contact in two novels co-written by Niven.
Poul Anderson contributes three works to the Man-Kzin Wars period and one work to one of Pournelle's war periods. Because of its emphasis on wars, the Codominium History seems to me to be a slightly lesser partner when compared with the longer, more broadly based future histories, like, e.g., a TV mini-series as against a series of feature films. Nevertheless, these are three American future histories in the Heinlein tradition.