"extensive influences" is a correct and usable phrase in written English.
It is typically used to describe the widespread or significant effects or impact that something has on a situation or person. Example: "The cultural exchange program had extensive influences on the students, broadening their perspectives and deepening their understanding of different cultures."
The fossil fuel industry has extensive influence over many world governments.
Meanwhile, following the agreement reached at Ṭāʾif, Syria also continued to exercise an extensive influence in Lebanon.
The struggle also poses a troublesome issue for the interim Iraqi government, which has been working to shrug off accusations that the Americans retain extensive influence.
My legal hero is someone whom I not only admire for their legal career, but also for the extensive influence they have had over my own.
The move has raised fears that Iran is trying to extend its already extensive influence in the political and economic life of Iraq.
Greek mythology has subsequently had extensive influence on the arts and literature of Western civilization, which fell heir to much of Greek culture.
Liang's periodical publications, especially, exerted an extensive influence on the Chinese people in the early years of the 20th century.
MONEY FOR NOTHING: INSIDE THE FEDERAL RESERVE Liev Schreiber narrates this documentary, written and directed by Jim Bruce, about the inside workings and extensive influence of the United States Federal Reserve.
These efforts countered the persona of the humble, oblivious naïf by detailing his assured single-mindedness and tracked the extensive influence his work exerted on several generations of vanguard artists, starting with Picasso and including Léger, Beckmann and the Surrealists.
The controversy also included other, non-Christian voices such as the Druze leader, Walid Jumblatt, a one-time ally of Damascus who has since denounced its extensive influence -- which has included reviewing members of Parliament and ministers.
