"deepened cooperation" is correct and usable in written English.
It can be used to describe an increase in collaboration between entities. For example, "The two countries have agreed to deepen their cooperation in the area of trade."
The former presidents François Mitterrand and Jacques Chirac deepened cooperation with Abu Dhabi through arms sales.
Recently, the two sides have further deepened cooperation in a range of areas, including the mutually reciprocal and beneficial economic and trade ties, more open and inclusive regional economic cooperation, a policy environment favorable to innovation and cooperation, and sectors such as energy, climate change, medical services, infrastructure and financial services.
The two leaders, however, also discussed deepening cooperation on military intelligence and counterterrorism, he said.
They cited the arrest as an example of deepening cooperation between Mexican and United States drug-enforcement officials.
Turkey's deepening cooperation with Israel was one of the most promising diplomatic developments in the Middle East over the past decade, said a senior administration official.
This objective must be sustained by strong political commitments to deepen cooperation necessary for the alliance to be prepared for current and future challenges.
PARIS — The International Energy Agency, a forum for developed economies, announced a series of steps Wednesday to deepen cooperation with three nations of growing importance to global energy markets: Russia, China and India.
For Electricité de France, the move would enable it to deepen cooperation in a joint venture with Vivendi Environnement in energy services.
"The trip will underscore the president's commitment to broadening and deepening cooperation between the United States and the people of sub-Saharan Africa to advance regional and global peace and prosperity".
But some officials, speaking only on the condition of anonymity, said the move was evidence of the two countries' deepening cooperation in efforts to prevail over a common threat.
Gen. James N. Mattis, met Mr. Karzai on Tuesday in Kandahar to coordinate the move on the airport, underscoring the deepening cooperation between the Americans and the forces that now control the city.
