"step up cooperation" is a correct and usable phrase in written English.
It means to increase or improve cooperation between individuals or groups. Example: The two countries agreed to step up cooperation in trade and security matters in order to strengthen their relationship.
Russia and NATO both desire to step up cooperation, but their approaches differ.
A8 New U.S.-China Drug Effort The United States and China agreed to step up cooperation in the fight against illegal drugs, especially heroin and methamphetamine.
Turkey last year shot down a Russian jet that strayed into its airspace, and Medvedev called for Russia and the west to step up cooperation.
To step up efforts to facilitate return of migrants not in need for international protection and step up cooperation on repatriation with Afghanistan, Bangladesh, Iraq and Pakistan.
In a joint statement, China and Afghanistan said they would step up cooperation in security and the fight against terrorism, as well as increase intelligence sharing.
Yugoslavia is under intense international pressure to step up cooperation with the United Nations tribunal ahead of a donors' conference on June 29 in Brussels.
Confronted by its provocative nuclear and missile tests, he secured international sanctions, stepped up cooperation with South Korea and Japan and even garnered some support from China, the North's closest friend.
In order clinch its E.U. candidacy status, Serbia stepped up cooperation on tracking down war-crime suspects, including handing over Ratko Mladic, the Bosnian Serb general accused of war crimes, to The Hague last year.
Nigeria has also stepped up cooperation with neighboring countries Chad, Cameroon and Niger, where Boko Haram has hidden fighters and attacked civilians, and the U.S. has expanded military support to the anti-Boko Haram effort.
And the WikiLeaks files also show the Saudis have stepped up cooperation with the US in flushing out militant financiers.
The two museums are also stepping up cooperation, coordinating their catalogs and Web sites, and sharing their expertise in storing and restoring artifacts.
