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The phrase "a much higher priority" is correct and usable in written English.
You can use it when discussing the importance or urgency of a task or issue in comparison to others.
Example: "In our current project, addressing customer feedback is a much higher priority than implementing new features."
Alternatives: "a significantly greater priority" or "a far more important priority".
Exact(46)
They are happy to give this "a much higher priority".
Debating solutions, rather than the science, was deemed a much higher priority.
Development aimed at detecting highly enriched uranium needs to be a much higher priority.
He said that he would make tax cuts "a much higher priority" than they have been.
Counter-terrorism is a much higher priority than other types of crimes".
Lowering the cost of single-application products, he said, is a much higher priority.
Similar(14)
And the need to be Internet- and global communications—savvy is a much, much higher priority today than it was a few years ago".
However, saving a life has much higher priority to most women than going through additional treatments that they many not need.
For the implemented SCS-CR scheme (for performance comparison with this study), the adopted value set of (ωAC_VI, ωAAC_VI) is taken to be (0.9, 0.1) as a typical case which prefers much higher priority of AC_VI than AAC_VI, and thus one expects much better performance for real-time video streams while reserving some basic level of fairness to non-real-time video streams.
"Guns and drugs were a lot more exciting and got much higher priority at D.O.J.," Ms. Pierson said of the seven years she was a prosecutor, starting in 1980.
First, it suggests that preventing violence should be given much higher priority than it is now.
More suggestions(15)
a much higher interest
a much higher order
a far higher priority
a much greater priority
a much bigger priority
a much higher level
a much higher prevalence
a much higher percentage
a much higher dose
a much higher value
a much higher likelihood
a much higher content
a much higher density
a much higher amount
a much higher profit
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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