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The phrase "approaches each with" is correct and usable in written English.
It can be used when describing how someone or something engages with different subjects or situations in a particular manner.
Example: "The teacher approaches each student with patience and understanding to ensure they grasp the material."
Alternatives: "treats each with" or "handles each with".
Exact(8)
But our research recognises the usefulness of manifold approaches, each with pros and cons for different situations.
Given that extrapolation is often required, we considered several approaches, each with advantages and disadvantages.
However, our analyses have shown that alternative prioritization approaches, each with different assumptions, are needed in targeting endangerment since they choose different sets of species (Figure S2) and priority areas (Figure 3); hotspots of richness, threat and endemism schemes vary greatly in their utility for conservation [17].
Further, this study uses two different statistical approaches, each with specific advantages.
The various combination treatments have led to several competing approaches, each with distinct advantages and disadvantages, and initial treatment can vary significantly between institutions.
OD methods comprise a wide variety of approaches, each with their own benefits and costs under a variety of evolutionary and practical scenarios.
Similar(52)
Williams ricochets around this jumble of subjects — approaching each with a distinct voice and posture — as if his mind had been turned inside out.
Vonn has a limited number of serious pursuits, but she tends to approach each with similar determination.
This has led to a large number of variants of the approach, each with its own merits.
Difficult and emotional issues to be sure, but I always try to approach each with a modicum of objectivity.
Cells are represented as individual entities (agent-based approach) each with their own cell cycle and subcellular-signalling machinery.
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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