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The phrase "upon which to run" is correct and usable in written English.
It can be used in contexts where you are referring to a foundation or basis for action, often in a metaphorical sense. Example: "We need to establish a solid framework upon which to run our new project effectively."
Exact(2)
There are only a handful of courses, and a handful of days, upon which to run fast.
We help them to Walk, give them a platform upon which to Run so that they can have the resources with which to Fly.
Similar(57)
As there was an absence of evidence upon which to base such guidance, we ran two separate literature searches for our review: one that included generic health terms and one that used more specific health terms.
It's predicated on the idea that running out of money is the key milestone upon which to base a fundraising.
There is no glimmer of hope upon which to cling.
upon which to expand.
There is common ground upon which to stand.
They are blank canvases upon which to build these characters.
Another key concept upon which to build greater understanding.
The brilliant minds of the punditry seem content to ignore this pattern or question it in any way, despite the fact that McCain is repeatedly screwing up the very platform upon which he claims to run.
"Nobody knew which direction to run.
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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