"make every possible effort" is a correct and usable phrase in written English.
You can use it when describing someone's attempt to do something with their utmost ability. For example: "Ivan made every possible effort to win the competition, but unfortunately, it was not enough."
As the crisis builds, he should make every possible effort to let the council take the lead.
Only a day earlier, Mr Arafat had pledged in a speech before the United Nations that he would make "every possible effort" to make peace.
To wit, 62 percent of blacks and 59 percent of Hispanics say that we should make every possible effort to improve the position of blacks and other minorities, even if it means giving them preferential treatment.
The Serbian government must make every possible effort to arrest two remaining indicted war crimes suspects — Gen. Ratko Mladic and Goran Hadzic — and deliver them to the Hague for trial.
"I believe the Ninth Circuit decision will be overturned by the United States Supreme Court, and I pledge to make every possible effort to achieve that result," Mr. Horne said.
Mr. Nixon's last formal exit speech was delivered at the White House on Aug. 8, 1974: Throughout the long and difficult period of Watergate, I have felt it was my duty to persevere; to make every possible effort to complete the term of office to which you elected me.
Mr. Feinberg has made every possible effort to reach out to the survivors.
I know I made every possible effort to provide essential services," he said.
"The Japanese police are making every possible effort to catch him.
He made the Medicare problem far worse when he should have been making every possible effort to improve its finances.
In its report, North Korea said it had made "every possible effort to eliminate terrorism in the world".
