Final answer:
The U.S. policy of expanding influence over overseas territories before the war with Spain in 1898 was known as expansionism. This marked a transition from isolationism to expansion-mindedness and the embrace of imperialism in the late 19th century.
Step-by-step explanation:
The policy that allowed the U.S. to enlarge its influence over overseas territories, whether economically or militarily, prior to the 1898 war with Spain was known as expansionism. This shift from isolationism to expansion-mindedness was influenced by late 19th-century developments, including industrial growth, the American West reaching its expansion limit, and a desire to compete with European powers on the global stage. The ideology was bolstered by the principles of influential figures such as Frederick J. Turner and Alfred Mahan. In practice, expansionism took form through the acquisition of territories such as Guam, Puerto Rico, and the Philippines after the Spanish-American War, which marked a departure from earlier practices where territories were incorporated with the potential for statehood and full citizenship rights. The adoption of an imperialistic approach, encompassing both political control and economic influence like the 'open door' policy with China, signified a significant transformation in America's global role.