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The phrase "already high levels" is correct and usable in written English.
It can be used when discussing measurements, quantities, or conditions that are currently elevated or above a certain threshold.
Example: "The study revealed that the population was experiencing already high levels of stress due to the ongoing crisis."
Alternatives: "previously elevated levels" or "currently high levels".
Exact(60)
The Algerian government has promised to step up the already high levels of security surrounding such plants.
Over the course of 2001, those changes should cause consumers to spend more money and even to add to their already high levels of debt.
Some contend that customers are taking zero percent in stride and that overall incentive spending is not increasing from its already high levels.
They have borrowed to survive from friends, from micro-credit companies and banks and from loan sharks, increasing already high levels of indebtedness.
This will have catastrophic consequences: significant devaluation, the collapse of the banking system, a massive rise in unemployment above already high levels.
The jobless rate in Germany was steady at 5.7percentt of the working population in February, while unemployment in southern Europe rose from already high levels.
Private-equity groups do not seem to be put off by the industry's already high levels of debt and its cyclical nature.
A dispute over whether tsunami emergency aid funds should be autonomously administered by the Tamil Tigers in their area of control meant that already high levels of distrust were further entrenched.
Low inflation added to the problems of the troubled countries on the fringes of the euro area, where it would increase the real burden of already high levels of public debt.
But unemployment jumped by 20,000 to 1.38 million following a difficult year for retailers with tens of thousands of high street workers made redundant, often in areas with already high levels of deprivation.
Sleep disturbances often persist for years and, when combined with already high levels of cancer-related distress, may place cancer survivors at a higher risk of future psychopathology, health problems and poorer quality of life.
More suggestions(16)
unfortunately high levels
yet high levels
already excessive levels
already high levies
ever high levels
still high levels
longer high levels
already substantial levels
prior high levels
actually high levels
leaves high levels
already high rate
earlier high levels
used high levels
already high expectations
had high levels
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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