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"largely exceeding" is a correct and usable phrase in written English.
You can use it when you are describing a quantity that is much larger than normal or expected. For example, "The increase in sales was largely exceeding our projections."
Exact(25)
It went up to £1.7 million, largely exceeding the high estimate.
The contact time was 1 h 30 min, largely exceeding the equilibrium time.
However, none of these events have had durations largely exceeding a year.
Pulsed magnets can produce magnetic fields largely exceeding those achieved with resistive or even hybrid magnets.
Only after the onset of rifting processes, uplift became active and transformed a vast lowland plain into the present Ethiopian highlands, largely exceeding 2500 m a.s.l.l
As the wet solidus for MOR basalts approaches such conditions (Fig. 1), epidote is expected to affect melting of mafic eclogites at pressures largely exceeding the amphibole stability field, therefore down to sub-arc depths.
Similar(35)
Usually, when data item is processed and transmitted across large-scale systems, the provenance size may largely exceeds the size of the data themselves; for example, Jayapandian et al. report that in the MiMI system, for data with size of 270 MB, the provenance for the data is approximately equal to 6 GB [12].
"Nu de dos, 4 état (Back IV)" as Christie's called it, largely exceeded its estimate as it climbed to a staggering $48.8 million.
The enemy is, of course, far more numerous than we are, but our new productions already, as I am advised, largely exceed his, and the American production is only just beginning to flow in.
Within amphibolite terrains, S largely exceeds 0.30 mhos and aquifers are less vulnerable to surface contamination.
The fluoride concentration largely exceeds 1.5 mg L−1, the recommended value by World Health Organization (WHO).
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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