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The phrase "a step by step basis" is correct and usable in written English.
It can be used when describing a method or approach that involves taking actions or making decisions incrementally or sequentially.
Example: "We will tackle the project on a step by step basis to ensure that each phase is completed thoroughly."
Alternatives: "incremental approach" or "gradual process".
Exact(3)
Traditional methods that calculate pavement data en masse would completely swamp a phone's processing ability, so instead, Roxon determines fuel consumption on a step by step basis.
Yesterday on CNN's "State of the Union" Sasse again called for an immediate vote on repealing the ACA but with a delay, so no one is "thrown off coverage". And Lee said that at this point, it would be easier to get repealing the law out of the way and then pass a replacement on a "step by step" basis.
In the 1996 campaign, after his grander ambitions failed, Clinton vowed to protect those federal programs and called for an expansion of health care on a "step by step" basis, only as the country could afford it — and he won back the issue.
Similar(57)
If it is a step-by-step basis, we should begin with the homeowners".
I think it's most important to go about this on a step-by-step basis".
"We have discussed how to improve our bilateral relations but it will have to take place on a step-by-step basis.
I'm asking for more time as I want to work on a step-by-step basis," regional police commander Lieutenant General Panya Mamen told the Phuket Gazette.
For each module, the implementation is described on a step-by-step basis including conceptual issues as well as logistics and methodological questions.
If you can't get 75 to 80 votes on something that is this important for this much reform, we should start over and do it on a step-by-step basis".
"Black-starting" a platform (i.e. restarting a platform when all of its operations had been fully shut down) was a very difficult, time-consuming process, and would have to be taken slowly, on a step-by-step basis.
Through the Clinton, Bush and Obama administrations, top officials and lawmakers supported sanctions and Ms. Aung San Suu Kyi, and, when they saw an opening in 2011, agreed to engage with Myanmar on a step-by-step basis.
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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