"Would you take me drunk?"
Is there an common way to understand this request?
(to give me a drink, to get a taxi for drunk me, or..?)

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One more observation.   Getting "drunk" is not what anyone "takes you to"  basically  because   one gets drunk by  drinking alcohol, and not be being "taken" by another person, you see?

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The sentence lacks logical coherence.  I cannot tell you that there would be a "common way"   to understand it because I have never seen such a sentence before.

It could mean any of the following.

Would you take me out drinking alcohol and get drunk with me?   or 
   Would you have  sex with me  while I am drunk?

I have not clue at all what this sentence actually means.

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