Wiki article on Alternative Histories. Alternative history fiction itself has a long history - its earliest origins were historical, even Roman - although HG Wells may have been the first writer to describe travel between alternative histories.
The article rightly states that it is impossible to discuss separately from each other alternative history fiction and time travel fiction in which history is changed. Thus, the article appropriately refers both to Poul Anderson's Time Patrol series (time travelers changing history) and to his Old Phoenix stories (travelers between alternative histories).
However, here is at least one culmination of this sub-genre:
SM Stirling's Draka series recounts an alternative history from 1779 to 2445 and also describes travel between histories;
the series comprises four novels by Stirling and one anthology of twelve stories by other authors, edited by Stirling;
Poul Anderson is quoted on the back cover of the anthology as commenting "...an exciting, evocative [and] horrifying read."
The twelve contributors to the anthology, Drakas! are:
William Sanders, writer of fantasy and sf, including alternative histories;
John Miller, author of graphic novels and of stories set in George RR Martin's Wild Cards alternative history series;
Roland Green who has continued H Beam Piper's Great King's War alternative history;
David Drake, author of the Hammer's Slammers future war series;
Jane Lindskold, a former professor of English;
Lee Allred, author of alternative history fiction;
William Barton, author of When We Were Real;
Harry Turtledove, often called the master of alternative history;
Anne Marie Talbott, published here for the first time;
Markus Baur, a high tech sector worker resident in Vienna;
John Barnes, who introduces his crosstime-travel hero, Mark Strang, to the Draka;
Severna Park, sf novelist.
Stirling explains the reasoning behind the series:
What were the good and bad consequences of European colonialism?
What if its worst consequence, slavery, had grown until it was unstoppable?
Thus, as I suspected, Draka world domination is part of the premise and has to be accepted as such.