This sentence works in Polish, but it is an example of a sentence that is too closely translated into English. A more natural translation would be "I want to cook with you."
How would you say, I want us to cook together. This is a more natural way to say it in English.
"Chcę byśmy/żebyśmy gotowali razem". (general, habitual - well, potentially habitual?)
Or maybe rather "ugotowali (coś) razem", to cook (something) succesfully together.
Why three finite verbs after one another? I would have thought "chcę ugotować...".
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