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The phrase "a method with which" is correct and usable in written English.
It can be used when describing a specific method or technique that is employed to achieve a particular result or outcome.
Example: "The researcher developed a method with which to analyze the data more effectively."
Alternatives: "a method for" or "a technique that allows".
Exact(18)
Working with Dr. Max Perutz and others, Dr. Blow helped devise a method with which X-rays could be passed through a crystallized sample of a given protein.
Rix believed that "a farce has to be played in one certain way", and it was a method with which Gray was in accord.
He was among the pioneers of the technique in the early '90s, while still a student at the University of Pennsylvania, working to develop a method with which to monitor the oxygenation of blood noninvasively and without ionizing radiation.
Objective: The purpose of this project was to study an in vitro model for plugging membrane defects with gelatin sponge and to develop a method with which to use this material to treat premature rupture of the membranes.
The methodology includes the design of a transmission experiment, and a method with which A. pleuropneumoniae transmission can be quantified and with which the effect of an intervention on the transmission can be tested.
Here we report a method with which to prepare Ca/P composite scaffolds with a pore structure and Ca/P distribution better suited to facilitate BMSC differentiation and bone formation.
Similar(42)
There is a need for an a priori method with which to demonstrate the physical similarities between non-classical bioisosteres.
Ac impedance at a microelectrode has proved to be a powerful method with which to study redox reactions in solid polymer systems characterised by low conductivity and diffusion coefficients.
If he/she says, "Yeah, it was a bit much" then you should probably opt for a subtler method with which to ask him/her to prom--potentially even just asking them in a straightforward way.
Moreover, DW is a promising method with which high long-term genetic gain can be expected within a fixed time frame.
Is there a general method with which you approach book design, or is each case different?
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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