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The phrase "are further deepened" is correct and usable in written English.
It can be used when discussing the enhancement or intensification of a particular situation, feeling, or relationship.
Example: "The connections between the team members are further deepened through collaborative projects and shared experiences."
Alternatives: "are further intensified" or "are further strengthened".
Dictionary
Exact(3)
The Portuguese's problems are further deepened by the prospect of losing his top scorer, Romelu Lukaku, for two matches because of a ninth-minute clash of heads with Wesley Hoedt.
In this scenario basins that were generated during normal tectonic extension are further deepened as a result of having substantial loads placed into them during the post-rift phase (Fig. 6).
Discrete tonalities or tonal strata, appearing in complete musical segregation from one another at the beginning of each sonata, suggest contrasting psychological states, such as reality and dream, home and exile, etc.; these conflicts are further deepened in the ensuing slow movements.
Similar(57)
The monastic life also offered physical retreat, which could be further deepened with a retreat into art.
This initiative will be further deepened by a series of related studies and publications based on the needs of individual countries.
But the hard sell failed to convince a deeply sceptical population whose doubts were further deepened with the violent death on February 5 of La Foca's lawyer, Mario Escobedo, who had put together an impressive defence, claiming the confessions were induced by torture and were internally contradictory.
With key referendums and elections due in the next 12 months in Austria, the Netherlands, Germany and France, the distrust, disillusion and even full-scale rejection of the political establishment already evident across much of Europe – and that risks being further deepened by each act of violence – could rock the continent's political foundations.
This reflection, which emerges from the current state of the study, may be further deepened through future research steps.
The development is further deepened along the so-called 'Internet of Things', where knowledge and information technology is embedded into artefacts and everywhere in the built environment.
The hole was further deepened in 2008 when Seattle's pro basketball team, the Supersonics upped sticks and relocated to Oklahoma City.
It seems the "special relationship" between Brits and Yanks will be further deepened this winter, thanks to a dose of empathy and soaring gas bills.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com