The phrase "acquire dominion" is correct and usable in written English.
It can be used in contexts discussing control, authority, or ownership over something, often in a formal or literary sense.
Example: "The empire sought to acquire dominion over the newly discovered lands to expand its influence."
Alternatives: "gain control" or "establish authority."
When the United States purchased Alaska from the Russian tsar and Canada acquired dominion status, both in 1867, European possessions on the American mainland were reduced to three small Guianan colonies in South America and British Honduras (Belize).
The lake was called Lacus Benacus by the classical writers Virgil, Horace, and Catullus; its name was changed when the city of Garda, elevated to a county in the early 9th century by the emperor Charlemagne, acquired dominion over the lake.
Soon after, he was forced out on military expeditions to secure the recently acquired dominions from Danish troops in the Scanian War.
Yet Hamilcar Barca sought to rebuild Carthaginian strength by acquiring a dominion in Spain where Carthage might gain new wealth and manpower.
11 15 A.M. (Sundance) RAN (1985) In his masterwork inspired by Shakespeare's "King Lear," the Japanese director Akira Kurosawa tells the story of Hidetora Ichimonji (Tatsuya Nakadai, below), an exhausted 70-year-old warlord who wants to turn the vast dominion acquired through 50 years of bloodshed over to his three sons, on whose kindness he will then depend.
11 A.M. (Sundance) RAN (1985) In his masterwork inspired by Shakespeare's "King Lear," the Japanese director Akira Kurosawa tells the story of Hidetora Ichimonji (Tatsuya Nakadai), an exhausted 70-year-old warlord who wants to turn the vast dominion acquired through 50 years of bloodshed over to his three sons, on whose kindness he will then depend.
Guns have been symbols of power utilized to acquire wealth, prestige and dominion.
Toronto-Dominion will acquire about $5.9 billion in net assets and $400 million in good will from Chrysler Financial, the former financing arm of the carmaker.
Knowing that Superman is the prime obstacle to his diabolical plot for world dominion, Lex acquires a trove of Kryptonite in order to create a weapon that will kill Superman and he seeks to stoke public and official enmity toward Superman so that the actual attack on the archetypal superhero will be undertaken by others.
