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The phrase "otherwise we would" is correct and commonly used in written English.
It is typically used to introduce a hypothetical situation or consequence that would occur if a certain condition were not met. Example: "We must finish this project by tomorrow, otherwise we would risk missing the deadline." In this sentence, "otherwise we would" expresses the potential outcome if the project is not completed on time. It is also common to use "otherwise" on its own, without the "we would" as in, "We must finish this project by tomorrow, otherwise we risk missing the deadline."
Exact(59)
We also presupposed that the sentence was jointly authored, for otherwise "we" would not have referred.
"Otherwise, we would go crazy".
Otherwise, we would not have been friends.
Otherwise we would have let them in.
Otherwise, we would not have known.
Otherwise, we would have suspected poison".
"Otherwise we would have lost – easily".
Otherwise, we would expect the mean yields to differ.
Otherwise we would have had a solution before now.
Otherwise, we would be talking about the genius of Tosatti.
Similar(1)
Otherwise we would be in an unhealthy "unequal yoking".
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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