The phrase "already cooperated with" is correct and usable in written English.
You can use it to indicate that collaboration or partnership has taken place prior to the current moment or context.
Example: "The team has already cooperated with several organizations to achieve their goals."
Alternatives: "previously collaborated with" or "have worked together with".
Some manufacturers have already cooperated with Latin NCAP, and legislation recently passed in Argentina and Brazil will require standard air bags by 2014, according to the group's report.
Israel's Channel 10 news reported that Talansky had already cooperated with Israeli investigators and detailed his role as a middleman for illegal campaign contributions.
The pharmacies invited to participate in the Dutch patient questionnaires were selected among all the pharmacies that already cooperated with the University of Groningen, Pharmacy (RuG-Pha).
Danrong Song, CNNC's chief designer for SMRs, attended an SMR conference in London in October and pitched a "technical plan and proposal for cooperation with UK industry" – the company is already cooperating with Rolls Royce.
"Our government is already cooperating with the U.S. — but they also must respect our sovereignty".
Unbeknown to Ms. Lewinsky, Mrs. Tripp was already cooperating with Mr. Starr, and she later gave him the talking points.
BMW, based in Munich, already cooperates with its German rival Daimler in buying some parts, and with the French carmaker PSA Peugeot Citroën on engines for smaller cars.
He added that he could have ordered Mr. Basciano killed, but that by that time he was already cooperating with the government.
One of the topless dancers is already cooperating with the government, and she is likely to testify against him at trial.
Europol, the fledgling European police agency, already cooperates with the Federal Bureau of Investigation on the grounds that the attacks in New York and Washington on Sept. 11 are seen as a life-threatening situation.
The buyer, an unnamed man who had pleaded guilty to securities fraud and was already cooperating with federal agents, called the United States attorney's office in Brooklyn in March and told investigators that Mr. Walsh had approached him trying to sell the five paintings.
