The phrase "deepen concern" is grammatically correct and can be used in written English.
It is often used to describe a situation where someone's level of worry or anxiety about something increases. Example: The recent spike in crime rates has deepened concern among the local community.
Indeed, the agreement may deepen concern among Sunni regimes fearful of Iran's reëmergence as a player rather than a pariah.
At a time when the relationship between publishers and Facebook is already tense, any change that de-emphasizes news content is likely to deepen concern.
But the targeting of sports officials is likely to deepen concern among Erdoğan's critics that the coup has sparked a disturbingly broad purge.
While NATO officials said it was normal practice to inform troops about hazardous materials, the warnings about depleted uranium are likely to deepen concern in Europe.
The military successes of Boko Haram will deepen concern that Nigeria's army, despite the bravery of individual soldiers and units, is unable to stop the rebel force despite pledges of military aid from London and Washington.
The move is likely to deepen concern among rights activists and Turkey's Western allies about its record on civil liberties under President Tayyip Erdogan's Islamist-rooted AK Party.
But investigators consider the documents significant because they deepen concerns about whether McNeil, responsible for a recall in April of an estimated 136 million bottles of pediatric medicines, was aboveboard in its handling of various quality-control problems.
The steady increase in marine debris arriving on Pacific shorelines as a result of the March 2011 tsunami in Japan is starting to tax state budgets as well as deepen concerns over invasive species.
Such prospects could deepen concerns at ratings agencies about Japan's ability to deal with its high public debt, which at more than twice the size of its $5 trillion economy is proportionally the heaviest among major industrialized nations.
In a move that will deepen concerns over the privatisation of justice contracts, Grayling announced that he had referred two more G4S contracts, involving facilities management for the courts, to the SFO to establish whether any dishonesty had taken place.
But the order on "Enhancing Public Safety in the Interior of the United States" certainly looks likely to deepen concerns about the legal robustness of the EU-US data transfer mechanism, given it's explicitly seeking to strip away privacy protections from non-U.S.
